Advertisements
Online Mock Tests
Chapters
![Balbharati solutions for Mathematics and Statistics 1 (Arts and Science) [English] 11 Standard Maharashtra State Board chapter 6 - Circle - Shaalaa.com](/images/mathematics-and-statistics-1-arts-and-science-english-11-standard-maharashtra-state-board_6:e3c01670e36a48e499844fcbaf828475.jpg "Balbharati solutions for Mathematics and Statistics 1 (Arts and Science) [English] 11 Standard Maharashtra State Board chapter 6 - Circle")
Advertisements
Solutions for Chapter 6: Circle
Below listed, you can find solutions for Chapter 6 of Maharashtra State Board Balbharati for Mathematics and Statistics 1 (Arts and Science) [English] 11 Standard Maharashtra State Board.
Balbharati solutions for Mathematics and Statistics 1 (Arts and Science) [English] 11 Standard Maharashtra State Board 6 Circle Exercise 6.1 [Page 129]
Find the equation of the circle with centre at origin and radius 4.
Find the equation of the circle with centre at (−3, −2) and radius 6.
Find the equation of the circle with centre at (2, −3) and radius 5.
Find the equation of the circle with centre at (−3, −3) passing through the point (−3, −6)
Find the centre and radius of the circle:
x2 + y2 = 25
Find the centre and radius of the circle:
(x − 5)2 + (y − 3)2 = 20
Find the centre and radius of the circle:
`(x - 1/2)^2 + (y + 1/3)^2 = 1/36`
Find the equation of the circle with centre at (a, b) touching the Y-axis
Find the equation of the circle with centre at (–2, 3) touching the X-axis.
Find the equation of the circle with centre on the X-axis and passing through the origin having radius 4.
Find the equation of the circle with centre at (3,1) and touching the line 8x − 15y + 25 = 0
Find the equation circle if the equations of two diameters are 2x + y = 6 and 3x + 2y = 4. When radius of circle is 9
If y = 2x is a chord of circle x2 + y2−10x = 0, find the equation of circle with this chord as diametre
Find the equation of a circle with radius 4 units and touching both the co-ordinate axes having centre in third quadrant.
Find the equation of circle (a) passing through the origin and having intercepts 4 and −5 on the co-ordinate axes
Find the equation of a circle passing through the points (1,−4), (5,2) and having its centre on the line x − 2y + 9 = 0
Balbharati solutions for Mathematics and Statistics 1 (Arts and Science) [English] 11 Standard Maharashtra State Board 6 Circle Exercise 6.2 [Page 132]
Find the centre and radius of the following:
x2 + y2 − 2x + 4y − 4 = 0
Find the centre and radius of the following:
x2 + y2 − 6x − 8y − 24 = 0
Find the centre and radius of the following:
4x2 + 4y2 − 24x − 8y − 24 = 0
Show that the equation 3x2 + 3y2 + 12x + 18y − 11 = 0 represents a circle
Find the equation of the circle passing through the points (5, 7), (6, 6) and (2, −2)
Show that the points (3, −2), (1, 0), (−1, −2) and (1, −4) are concyclic
Balbharati solutions for Mathematics and Statistics 1 (Arts and Science) [English] 11 Standard Maharashtra State Board 6 Circle Exercise 6.3 [Page 135]
Write the parametric equations of the circle:
x2 + y2 = 9
Write the parametric equations of the circle:
x2 + y2 + 2x − 4y − 4 = 0
Write the parametric equations of the circle:
(x − 3)2 + (y + 4)2 = 25
Find the parametric representation of the circle:
3x2 + 3y2 − 4x + 6y − 4 = 0
Find the equation of a tangent to the circle x2 + y2 − 3x + 2y = 0 at the origin
Show that the line 7x − 3y − 1 = 0 touches the circle x2 + y2 + 5x − 7y + 4 = 0 at point (1, 2)
Find the equation of tangent to the circle x2 + y2 − 4x + 3y + 2 = 0 at the point (4, −2)
Balbharati solutions for Mathematics and Statistics 1 (Arts and Science) [English] 11 Standard Maharashtra State Board 6 Circle Miscellaneous Exercise 6 [Pages 136 - 138]
Choose the correct alternative:
Equation of a circle which passes through (3, 6) and touches the axes is
x2 + y2 + 6x + 6y + 3 = 0
x2 + y2 − 6x − 6y − 9 = 0
x2 + y2 − 6x − 6y + 9 = 0
x2 + y2 − 6x + 6y − 3 = 0
Choose the correct alternative:
If the lines 2x − 3y = 5 and 3x − 4y = 7 are the diameters of a circle of area 154 sq. units, then find the equation of the circle
x2 + y2 − 2x + 2y = 40
x2 + y2 − 2x + 2y = 40
x2 + y2 − 2x + 2y = 47
x2 + y2 − 2x − 2y = 40
Choose the correct alternative:
Find the equation of the circle which passes through the points (2, 3) and (4, 5) and the centre lies on the straight line y − 4x + 3 = 0
x2 + y2 − 4x − 10y + 25 = 0
x2 + y2 − 4x − 10y − 25 = 0
x2 + y2 − 4x + 10y − 25 = 0
x2 + y2 + 4x − 10y + 25 = 0
Choose the correct alternative:
The equation of the tangent to the circle x2 + y2 = 4 which are parallel to x + 2y + 3 = 0 are
x − 2y = 2
x + 2y = `± 2sqrt(3)`
x + 2y = `± 2sqrt(5)`
x − 2y = `± 2sqrt(5)`
Choose the correct alternative:
If the lines 3x − 4y + 4 = 0 and 6x − 8y − 7 = 0 are tangents to a circle, then find the radius of the circle
`3/4`
`4/3`
`1/4`
`7/4`
Choose the correct alternative:
Area of the circle centre at (1, 2) and passing through (4, 6) is
5π
10π
25π
100π
Choose the correct alternative:
If a circle passes through the point (0, 0), (a, 0) and (0, b) then find the co-ordinates of its centre
`((-"a")/2, (-"b")/2)`
`("a"/2, (-"b")/2)`
`((-"a")/2, "b"/2)`
`("a"/2, "b"/2)`
Choose the correct alternative:
The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length 3a is
x2 + y2 = 9a2
x2 + y2 = 16a2
x2 + y2 = 4a2
x2 + y2 = a2
Choose the correct alternative:
A pair of tangents are drawn to a unit circle with center at the origin and these tangents intersect at A enclosing an angle of 60°. The area enclosed by these tangents and the area of the circle is
`2/sqrt(3) - pi/6`
`sqrt(3) - pi/3`
`pi/3 - sqrt(3)/6`
`sqrt(3)(1 - pi/6)`
Choose the correct alternative:
The parametric equations of the circle x2 + y2 + mx + my = 0 are
x = `(-"m")/2 + "m"/sqrt(2)costheta, y = (-"m")/2 + "m"/sqrt(2)sintheta`
x = `(-"m")/2 + "m"/sqrt(2)costheta, y = (+"m")/2 + "m"/sqrt(2)sintheta`
x = 0 , y = 0
x = mcosθ ; y = msinθ
Answer the following :
Find the centre and radius of the circle x2 + y2 − x +2y − 3 = 0
Answer the following :
Find the centre and radius of the circle x = 3 – 4 sinθ, y = 2 – 4cosθ
Answer the following :
Find the equation of circle passing through the point of intersection of the lines x + 3y = 0 and 2x − 7y = 0 whose centre is the point of intersection of lines x + y + 1 = 0 and x − 2y + 4 = 0
Answer the following :
Find the equation of circle which passes through the origin and cuts of chords of length 4 and 6 on the positive side of x-axis and y-axis respectively
Answer the following :
Show that the points (9, 1), (7, 9), (−2, 12) and (6, 10) are concyclic
The line 2x − y + 6 = 0 meets the circle x2 + y2 + 10x + 9 = 0 at A and B. Find the equation of circle on AB as diameter.
Show that x = −1 is a tangent to circle x2 + y2 − 2y = 0 at (−1, 1).
Answer the following :
Find the equation of tangent to the circle x2 + y2 = 64 at the point `"P"((2pi)/3)`
Answer the following:
Find the equation of locus of the point of intersection of perpendicular tangents drawn to the circle x = 5 cos θ and y = 5 sin θ
Answer the following :
Find the equation of the circle concentric with x2 + y2 – 4x + 6y = 1 and having radius 4 units
Answer the following :
Find the lengths of the intercepts made on the co-ordinate axes, by the circle:
x2 + y2 – 8x + y – 20 = 0
Answer the following :
Find the lengths of the intercepts made on the co-ordinate axes, by the circle:
x2 + y2 – 5x + 13y – 14 = 0
Answer the following :
Show that the circles touch each other externally. Find their point of contact and the equation of their common tangent:
x2 + y2 – 4x + 10y +20 = 0,
x2 + y2 + 8x – 6y – 24 = 0.
Answer the following :
Show that the circles touch each other externally. Find their point of contact and the equation of their common tangent:
x2 + y2 – 4x – 10y + 19 = 0,
x2 + y2 + 2x + 8y – 23 = 0.
Answer the following :
Show that the circles touch each other internally. Find their point of contact and the equation of their common tangent:
x2 + y2 – 4x – 4y – 28 = 0,
x2 + y2 – 4x – 12 = 0
Answer the following :
Show that the circles touch each other internally. Find their point of contact and the equation of their common tangent:
x2 + y2 + 4x – 12y + 4 = 0,
x2 + y2 – 2x – 4y + 4 = 0
Answer the following :
Find the length of the tangent segment drawn from the point (5, 3) to the circle x2 + y2 + 10x – 6y – 17 = 0
Answer the following :
Find the value of k, if the length of the tangent segment from the point (8, –3) to the circle
x2 + y2 – 2x + ky – 23 = 0 is `sqrt(10)`
Answer the following :
Find the equation of tangent to Circle x2 + y2 – 6x – 4y = 0, at the point (6, 4) on it
Answer the following :
Find the equation of tangent to Circle x2 + y2 = 5, at the point (1, –2) on it
Answer the following :
Find the equation of the tangent to Circle x = 5 cosθ. y = 5 sinθ, at the point θ = `pi/3` on it
Answer the following :
Show that 2x + y + 6 = 0 is a tangent to x2 + y2 + 2x – 2y – 3 = 0. Find its point of contact
Answer the following :
If the tangent at (3, –4) to the circle x2 + y2 = 25 touches the circle x2 + y2 + 8x – 4y + c = 0, find c
Answer the following :
Find the equations of the tangents to the circle x2 + y2 = 16 with slope –2
Answer the following :
Find the equations of the tangents to the circle x2 + y2 = 4 which are parallel to 3x + 2y + 1 = 0
Answer the following :
Find the equations of the tangents to the circle x2 + y2 = 36 which are perpendicular to the line 5x + y = 2
Answer the following :
Find the equations of the tangents to the circle x2 + y2 – 2x + 8y – 23 = 0 having slope 3
Answer the following :
Find the equation of the locus of a point, the tangents from which to the circle x2 + y2 = 9 are at right angles.
Answer the following :
Tangents to the circle x2 + y2 = a2 with inclinations, θ1 and θ2 intersect in P. Find the locus of such that tan θ1 + tan θ2 = 0
Answer the following :
Tangents to the circle x2 + y2 = a2 with inclinations, θ1 and θ2 intersect in P. Find the locus of such that cot θ1 + cot θ2 = 5
Answer the following :
Tangents to the circle x2 + y2 = a2 with inclinations, θ1 and θ2 intersect in P. Find the locus of such that cot θ1 . cot θ2 = c
Solutions for 6: Circle
Balbharati solutions for Mathematics and Statistics 1 (Arts and Science) [English] 11 Standard Maharashtra State Board chapter 6 - Circle
Shaalaa.com has the Maharashtra State Board Mathematics Mathematics and Statistics 1 (Arts and Science) [English] 11 Standard Maharashtra State Board Maharashtra State Board solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. Balbharati solutions for Mathematics Mathematics and Statistics 1 (Arts and Science) [English] 11 Standard Maharashtra State Board Maharashtra State Board 6 (Circle) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.
Further, we at Shaalaa.com provide such solutions so students can prepare for written exams. Balbharati textbook solutions can be a core help for self-study and provide excellent self-help guidance for students.
Concepts covered in Mathematics and Statistics 1 (Arts and Science) [English] 11 Standard Maharashtra State Board chapter 6 Circle are Different Forms of Equation of a Circle, General Equation of a Circle, Parametric Form of a Circle, Tangent, Condition of tangency, Tangents from a Point to the Circle, Director circle.
Using Balbharati Mathematics and Statistics 1 (Arts and Science) [English] 11 Standard Maharashtra State Board solutions Circle exercise by students is an easy way to prepare for the exams, as they involve solutions arranged chapter-wise and also page-wise. The questions involved in Balbharati Solutions are essential questions that can be asked in the final exam. Maximum Maharashtra State Board Mathematics and Statistics 1 (Arts and Science) [English] 11 Standard Maharashtra State Board students prefer Balbharati Textbook Solutions to score more in exams.
Get the free view of Chapter 6, Circle Mathematics and Statistics 1 (Arts and Science) [English] 11 Standard Maharashtra State Board additional questions for Mathematics Mathematics and Statistics 1 (Arts and Science) [English] 11 Standard Maharashtra State Board Maharashtra State Board, and you can use Shaalaa.com to keep it handy for your exam preparation.
