English

Find the Equation of the Circle With: Centre (A, A) and Radius √ 2 A. - Mathematics

Advertisements
Advertisements

Question

Find the equation of the circle with:

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

Advertisements

Solution

Here, h = a, = a and radius  =\[\sqrt{2}a\]

∴ Required equation of the circle:

\[\left( x - a \right)^2 + \left( y - a \right)^2 = \left( \sqrt{2}a \right)^2\]
\[\Rightarrow x^2 + a^2 - 2ax + y^2 + a^2 - 2ay = 2 a^2 \]
\[ \Rightarrow x^2 + y^2 - 2ay - 2ax = 0\]
shaalaa.com
Advanced Concept of Circle - Standard Equation of a Circle
  Is there an error in this question or solution?
Chapter 24: The circle - Exercise 24.1 [Page 21]

APPEARS IN

RD Sharma Mathematics [English] Class 11
Chapter 24 The circle
Exercise 24.1 | Q 1.5 | Page 21

RELATED QUESTIONS

Find the equation of the circle with:

Centre (−2, 3) and radius 4.


Find the equation of the circle with:

Centre (0, −1) and radius 1.


Find the equation of the circle with:

Centre (a cos α, a sin α) and radius a.


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

(x + 5)2 + (y + 1)2 = 9


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

x2 + y2 − 4x + 6y = 5


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

x2 + y2 − x + 2y − 3 = 0.


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


Find the equation of the circle which has its centre at the point (3, 4) and touches the straight line 5x + 12y − 1 = 0.


Find the equation of the circle which touches the axes and whose centre lies on x − 2y = 3.


A circle of radius 4 units touches the coordinate axes in the first quadrant. Find the equations of its images with respect to the line mirrors x = 0 and y = 0.


If the lines 3x − 4y + 4 = 0 and 6x − 8y − 7 = 0 are tangents to a circle, then find the radius of  the circle.


Show that the point (xy) given by  \[x = \frac{2at}{1 + t^2}\] and \[y = a\left( \frac{1 - t^2}{1 + t^2} \right)\]  lies on a circle for all real values of t such that \[- 1 \leq t \leq 1\] where a is any given real number.

 


The circle x2 + y2 − 2x − 2y + 1 = 0 is rolled along the positive direction of x-axis and makes one complete roll. Find its equation in new-position.


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 coordinates of the centre and radius of each of the following circles:  x2 y2 − ax − by = 0


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)


Find the equation of the circle which passes through (3, −2), (−2, 0) and has its centre on the line 2x − y = 3.


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


ABCD is a square whose side is a; taking AB and AD as axes, prove that the equation of the circle circumscribing the square is x2 + y2 − a (x + y) = 0.


The line 2x − y + 6 = 0 meets the circle x2 + y2 − 2y − 9 = 0 at A and B. Find the equation of the circle on AB as diameter.


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.


If the radius of the circle x2 + y2 + ax + (1 − a) y + 5 = 0 does not exceed 5, write the number of integral values a.


If the equation of a circle is λx2 + (2λ − 3) y2 − 4x + 6y − 1 = 0, then the coordinates of centre are


The equation x2 + y2 + 2x − 4y + 5 = 0 represents


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


The equation of the circle passing through the point (1, 1) and having two diameters along the pair of lines x2 − y2 −2x + 4y − 3 = 0, 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


The equation of the incircle formed by the coordinate axes and the line 4x + 3y = 6 is


If the point (λ, λ + 1) lies inside the region bounded by the curve \[x = \sqrt{25 - y^2}\] and y-axis, then λ belongs to the interval


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


Equation of the circle through origin which cuts intercepts of length a and b on axes is


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


Equation of the circle with centre on the y-axis and passing through the origin and the point (2, 3) is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×