Advertisements
Advertisements
प्रश्न
Find the equation of the circle with centre at (−3, −3) passing through the point (−3, −6)
उत्तर
Centre of the circle is C (– 3, – 3) and it passes through the point P (– 3, – 6).
By distance formula
Radius (r) = CP = `sqrt([-3 - (-3)]^2 + [- 6 - (- 3)]^2`
= `sqrt((-3 + 3)^2 + (-6 + 3)^2`
= `sqrt(0^2 + (-3)^2`
= `sqrt(9)`
= 3
The equation of a circle with centre at (h, k) and radius ‘r’ is given by
(x – h)2 + (y – k)2 = r2
Here, h = – 3, k = –3, r = 3
∴ The required equation of the circle is
[x – (– 3)]2 + [y – (– 3)]2 = 32
∴ (x + 3)2 + (y + 3)2 = 9
∴ x2 + 6x + 9 + y2 + 6y + 9 – 9 = 0
∴ x2 + y2 + 6x + 6y + 9 = 0.
APPEARS IN
संबंधित प्रश्न
Find the equation of the circle with centre at origin and radius 4.
Find the equation of the circle with centre at (2, −3) and radius 5.
Find the centre and radius of the circle:
x2 + y2 = 25
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 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 of a circle with radius 4 units and touching both the co-ordinate axes having centre in third quadrant.
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
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
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
Choose the correct alternative:
Area of the circle centre at (1, 2) and passing through (4, 6) is
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.
Answer the following :
Find the equation of the circle concentric with x2 + y2 – 4x + 6y = 1 and having radius 4 units
The centre of the circle x = 3 + 5 cos θ, y = - 4 + 5 sin θ, is ______
The radius of a circle is increasing uniformly at the rate of 2.5cm/sec. The rate of increase in the area when the radius is 12cm, will be ______
If x2 + (2h - 1)xy + y2 - 24x - 8y + k = 0 is the equation of the circle and 12 is the radius of the circle, then ______.
The equation of circle whose diameter is the line joining the points (–5, 3) and (13, –3) is ______.
Circle x2 + y2 – 4x = 0 touches ______.
The equation of a circle with centre at (1, 0) and circumference 10π units is ______.
Let AB be a chord of the circle x2 + y2 = r2 subtending a right angle at the centre, then the locus of the centroid of the ΔPAB as P moves on the circle is ______.
