Question

 

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

Solution

Correct option is

 

The given circles are  

           x2 + y2 + 13x – 3y = 0                    …(i)

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

  

Equation of any circle passing through the point of intersection of the circles (1) and (2) is  

(x2 + y2 + 13x – 3y) + λ

 It passes through (1, 1) then

         (1 + 1 + 13 – 3) +   

  

                                

Substituting the value of λ in (3), the required equation is  

              

SIMILAR QUESTIONS

Q1

 

The angle between a pair of tangents from a point P to the circle

     x2 + y2 + 4x – 6y + 9 sin2α + 13 cos2α = 0 is 2α.

Find the equation of the lows of the point P.   

Q2

 

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

     2x2 + 2y2 – 7x – 9y – 30 = 0   

Q3

 

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. 

Q4

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.

Q5

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

Q6

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

Q7

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.

Q8

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

Q9

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.

Q10

 

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.