Question

Find the equation of circle through points of intersection of circle x2 + y2– 2x – 4y + 4 = 0 and the line x + 2y = 4 which touches the line x + 2y = 0.

Solution

Correct option is

x2 + y2 – x – 2y = 0

 

Equation of any circle through points of intersection of the given circle and the line is 

       

      

It will touch the line x + 2y = 0 if solution of equation (1) and x = –2y be unique.  

Hence the roots of the equation  

      

     

Must be equal.  

Then         0 – 4.5.4(1 – λ) = 0 or 1 – λ = 0 or λ = 1  

From (1), the required circle is x2 + y2 – x – 2y = 0.

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 thouchese x2 + y2 = e2 find ab in.

Q2

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

Q3

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

Q4

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.

Q5

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

Q6

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.

Q7

 

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

Q8

 

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.

Q9

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.

Q10

Find the angle between the circles. S = x2 + y2 – 4x + 6y + 11 = 0 and