Question

 

Find the equation of circle passing through the point of intersection of the circle x2 + y2 – 6x + 2y + 4 = 0 and x2 + y2 + 2x – 4y – 6 = 0 and whose centre lies on the line y = x.

Solution

Correct option is

7x2 + 7y2 – 10x – 10y – 12 = 0

 

Equation of any circle through the points of intersection of given circles is   

          (x2 + y2 – 6x + 2y + 4) + λ(x2 + y2 + 2x – 4y – 6) = 0  

⇒   x2(1 + λ) + y2 (1 + λ) – 2x(3 – λ) + 2y (1 – 2λ) + (4 – 6λ) = 0 

  

  

  

  

∴ Substituting the value of λ = 4/3 in (1), we get the require equation is

                  7x2 + 7y2 – 10x – 10y – 12 = 0.

SIMILAR QUESTIONS

Q1

 

Find the length of tangents drawn from the point (3, – 4) to the circle

     2x2 + 2y2 – 7x – 9y – 30 = 0   

Q2

 

Find the condition that chord of contact of any external point (hk) to the circle x2 + y2 = a2 should subtend right angle at the centre of the circle. 

Q3

The chord of contact of tangents drawn from a point on the circle x2 +y2 = a2 to the circle x2 + y2 = b2 thouchese x2 + y2 = e2 find ab in.

Q4

Find the middle point of the chord intercepted on line lx + my + n = 0 by the circle x2 + y2 = a2.

Q5

Find the equation of the tangents from the point A(3, 2) to the circle x2 +y2 + 4x + 6y + 8 = 0.

Q6

If two tangents are drawn from a point on the circle x2 + y2 = 25 to the circle x2 + y2 = 25. Then find the angle between the tangents.

Q7

Find the equation of diameter of the circle x2 + y2 + 2gx + 2fy + c = 0 which corresponds o the chord ax + by + λ = 0. 

Q8

Examine if the two circle x2 + y2 – 2x – 4y = 0 and x2 + y2 – 8y – 4 = 0 touch each other externally or internally. Also the pointed contact.

Q9

 

Find the equation of the circle passing through (1, 1) and the point of intersection of circles.

         x2 + y2 + 13x – 3y = 0 and 2x2 + 2y2 + 4x – 7y – 25 = 0

Q10

Find the equation of the circle passing through the points of intersection of the circles x2 + y2 – 2x – 4y – 4 = 0 and x2 + y2 – 10x – 12y – 40 = 0.