Question

Find the equations of the circle which passes through the origin and cut off chords of length a from each of the lines y = x and y = –x.

Solution

Correct option is

 

Let the required circle be

                    x2 + y2 + 2gx + 2fy + c = 0   

which passes through (0, 0) then = 0  

∴                 x2 + y2 + 2gx + 2fy = 0                       …(1)

Point of intersection of the circle (1) and the line y = x are obtained by solving

                   x2 + x2 + 2gx + 2fx = 0  

  

  

These point are A(0, 0) and B(–g, –f, –g – f ) 

  

   

Similarly points of intersection of the circle (1) and the line

y = –x are C(0, 0) and D(f – gg – f

   

   

∴ Required equations are

            

SIMILAR QUESTIONS

Q1

Find the radical axis of co-axial system of circles whose limiting points are (–1, 2) and (2, 3).

Q2

Find the equation of the circle which passes through the origin and belongs to the co-axial of circles whose limiting points are (1, 2) and (4, 3).

Q3

Find the equation of the image of the circle x2 + y2 + 16x – 24y + 183 = 0 by the line mirror 4x + 7y + 13 = 0.

Q4

Find the area of the triangle formed by the tangents drawn from the point (4, 6) to the circle x2 + y2 = 25 and their chord of contact. Also find the length of chord of contact.

Q5

 

Find the lengths of external and internal common tangents to two circlesx2 + y2 + 14x – 4y + 28 = 0 and x2 + y2 – 14x + 4y – 28 = 0.      

 

Q6

Find the lengths of common tangents of the circles x2 + y2 = 6x and x2 +y2 + 2x = 0.  

Q7

 

Find the equation of the circle circumscribing the triangle formed by the lines:

         x + y = 6, 2x + y = 4 and x + 2y = 5,

Without finding the vertices of the triangle.

Q8

Find the equation of the circle circumscribing the quadrilateral formed by the lines in order are 5x + 3y – 9 = 0, x – 3y = 0, 2x – y = 0, x + 4y – 2 = 0 without finding the vertices of quadrilateral.

Q9

Find the equation of a circle which touches the x-axis and the line 4x – 3y+ 4 = 0. Its centre lies in the third quadrant and lies on the line x – y – 1 = 0.

Q10

Determine the radius of the circle, two of whose tangents are the lines 2x+ 3y – 9 = 0 and 4x + 6y + 19 = 0.