हिंदी

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

Advertisements
Advertisements

प्रश्न

Find the equation of the circle with:

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

Advertisements

उत्तर

Here, h = a, k = 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
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 24: The circle - Exercise 24.1 [पृष्ठ २१]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
अध्याय 24 The circle
Exercise 24.1 | Q 1.5 | पृष्ठ २१

संबंधित प्रश्न

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

x2 + y2 − x + 2y − 3 = 0.


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 equations of the circles touching y-axis at (0, 3) and making an intercept of 8 units on the X-axis.


Find the equations of the circles passing through two points on Y-axis at distances 3 from the origin and having radius 5.


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.


Show that the point (x, y) 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.

 


If the line 2x − y + 1 = 0 touches the circle at the point (2, 5) and the centre of the circle lies on the line x + y − 9 = 0. Find the equation of the circle.


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


Show that the points (3, −2), (1, 0), (−1, −2) and (1, −4) are concyclic.


Prove that the centres of the three circles x2 + y2 − 4x − 6y − 12 = 0, x2 + y2 + 2x + 4y − 10 = 0 and x2 + y2 − 10x − 16y − 1 = 0 are collinear.


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


If a circle passes through the point (0, 0),(a, 0),(0, b) then find the coordinates of its centre.


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 y - 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.


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 equation of the unit circle concentric with x2 + y2 − 8x + 4y − 8 = 0.


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.


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


If 2x2 + λxy + 2y2 + (λ − 4) x + 6y − 5 = 0 is the equation of a circle, then its radius is


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


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


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


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 concentric with x2 + y2 − 3x + 4y − c = 0 and passing through (−1, −2) is


The circle x2 + y2 + 2gx + 2fy + c = 0 does not intersect x-axis, if


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 the circles x2 + y2 = a and x2 + y2 − 6x − 8y + 9 = 0, touch externally, then a =


If the circles x2 + y2 + 2ax + c = 0 and x2 + y2 + 2by + c = 0 touch each other, then


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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×