Question

 

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

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

Solution

Correct option is

 

The given circles are

                      

   

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

     

Its passes through (1, 1) then

            

   

   

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

            

  

SIMILAR QUESTIONS

Q1

The chord of contact of tangents drawn from a point on the circle x2 +y2 = a2 to the circle x2 + y2 = b2 touches the circle x2 = y2 = c2. Show that abc are in GP.

Q2

Find the equation of the chord x2 + y2 – 6x + 10y – 9 = 0 which is bisected at (–2, 4).

Q3

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

Q4

Find the locus of middle points of chords of the circle x2 + y2 = a2, which subtend right angle at the point (c, 0).

Q5

Find the equations of the tangents from the point A(3, 2) to the circle x2y2 + 4x + 6y + 8 = 0 .

Q6

If two tangents are drawn from a point on the circle x2 + y2 = 50 to the circle x2 + y2 = 25 then find the angle between the tangents.

Q7

 

Find the equation of the diameter of the circle

x2 + y2 + 2gx + 2fy + c = 0 which corresponds to the chord ax = by + d= 0.

Q8

Find the locus of the pole of the line lx + my + n = 0 with respect to the circle which touches y-axis at the origin.

Q9

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

Q10

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