हिंदी

Find the Equation of the Circle With:Centre (0, −1) and Radius 1. - Mathematics

Advertisements
Advertisements

प्रश्न

Find the equation of the circle with:

Centre (0, −1) and radius 1.

उत्तर

 Here, h = 0, = −1 and radius = 1

∴ Required equation of the circle:

\[\left( x - 0 \right)^2 + \left( y + 1 \right)^2 = \left( 1 \right)^2\]
\[\Rightarrow x^2 + y^2 + 2y = 0\]
shaalaa.com
Circle - Standard Equation of a Circle
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 24: The circle - Exercise 24.1 [पृष्ठ २१]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
अध्याय 24 The circle
Exercise 24.1 | Q 1.3 | पृष्ठ २१

संबंधित प्रश्न

Find the equation of the circle with:

Centre (aa) and radius \[\sqrt{2}\]a.


Find the centre and radius of each of the following circles:

(x + 5)2 + (y + 1)2 = 9


If the equations of two diameters of a circle are 2x + y = 6 and 3x + 2y = 4 and the radius is 10, find the equation of the circle.


Find the equation of a circle
which touches both the axes and passes through the point (2, 1).


If the lines 2x  3y = 5 and 3x − 4y = 7 are the diameters of a circle of area 154 square units, then obtain the equation of the circle.


Find the equation of the circle having (1, −2) as its centre and passing through the intersection of the lines 3x + y = 14 and 2+ 5y = 18.


Find the coordinates of the centre and radius of each of the following circles:  x2 + y2 + 6x − 8y − 24 = 0


Find the coordinates of the centre and radius of each of the following circles: 2x2 + 2y2 − 3x + 5y = 7


Find the equation of the circle passing through the points:

(5, 7), (8, 1) and (1, 3)


Find the equation of the circle passing through the points:

 (5, −8), (−2, 9) and (2, 1)


Find the equation of the circle passing through the points:

 (0, 0), (−2, 1) and (−3, 2)


Show that the points (5, 5), (6, 4), (−2, 4) and (7, 1) all lie on a circle, and find its equation, centre and radius.


Find the equation of the circle which circumscribes the triangle formed by the lines

 x + y = 2, 3x − 4y = 6 and x − y = 0.


Find the equation of the circle which passes through the origin and cuts off chords of lengths 4 and 6 on the positive side of the x-axis and y-axis respectively.


Find the equation of the circle concentric with x2 + y2 − 4x − 6y − 3 = 0 and which touches the y-axis.


The sides of a square are x = 6, x = 9, y = 3 and y = 6. Find the equation of a circle drawn on the diagonal of the square as its diameter.


Find the equation of the circle which passes through the origin and cuts off intercepts aand b respectively from x and - axes.


The abscissae of the two points A and B are the roots of the equation x2 + 2ax − b2 = 0 and their ordinates are the roots of the equation x2 + 2px − q2 = 0. Find the equation of the circle with AB as diameter. Also, find its radius.


Find the equation of the circle which circumscribes the triangle formed by the lines x = 0, y = 0 and lx + my = 1.


Write the length of the intercept made by the circle x2 + y2 + 2x − 4y − 5 = 0 on y-axis.


Write the area of the circle passing through (−2, 6) and having its centre at (1, 2).


If the equation (4a − 3) x2 + ay2 + 6x − 2y + 2 = 0 represents a circle, then its centre is ______. 


If the centroid of an equilateral triangle is (1, 1) and its one vertex is (−1, 2), then the equation of its circumcircle is


If the point (2, k) lies outside the circles x2 + y2 + x − 2y − 14 = 0 and x2 + y2 = 13 then k lies in the interval


If the circles x2 + y2 = 9 and x2 + y2 + 8y + c = 0 touch each other, then c is equal to


The equation of the circle which touches the axes of coordinates and the line \[\frac{x}{3} + \frac{y}{4} = 1\] and whose centres lie in the first quadrant is x2 + y2 − 2cx − 2cy + c2 = 0, where c is equal to


If (x, 3) and (3, 5) are the extremities of a diameter of a circle with centre at (2, y), then the values of x and y are


The equation of the circle circumscribing the triangle whose sides are the lines y = x + 2, 3y = 4x, 2y = 3x is ______.


Equation of a circle which passes through (3, 6) and touches the axes is ______.


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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×