Question

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

Solution

Correct option is

x2 + y2 + 32x + 4y + 235 = 0

 

The given circle and line are

            x2 + y2 + 16x – 24y + 183 = 0              …(i)

and      4x + 7y + 13 = 0                                   …(ii)

Centre and radius of circle (i) are (–8, 12) and 5 respectively. Let the centre of the imaged circle be (x1y1).  

Hence (x1y1) be the image of the point (–8, 12) with respect to the line 4x + 7y + 13 = 0 then

             

             

    

∴ Equation of the imaged circle is  

           (x – 16)2 + (y + 2)2 = 52

           x2 + y2 + 32x + 4y + 235 = 0.

SIMILAR QUESTIONS

Q1

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.

Q2

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

Q3

 

Find the equation of the system of circles coaxial with the circles.

              x2 + y2 + 4x + 2y + 1 = 0, x2 + y2 – 2x + 6y – 6 = 0

Also find the equation of that particular circle whose centre lies on radical axis.

Q4

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

Q5

 

Find the circle whose diameter is the common chord of the circles

x2 + y2 + 2x + 3y + 1 = 0 and x2 + y2 + 4x + 3y + 2 = 0 

S ≡ x2 + y2 + 2x + 3y + 1 = 0 S’ ≡ x2 + y2 + 4x + 3y + 2 = 0

Q6

Find the equation of circle which cuts the circle x2 + y2 + 5x + 7y + 4 = 0 orthogonally, has its centre on the line x = 2, and passes through the point (4, –1).

Q7

Find the point of intersection of the line 2x + 3y = 18 and the circle x2 +y2 = 25.

Q8

Find the equation of the normal to the circle x2 + y2 – 5x + 2y – 48 = 0 at point (5, 6).

Q9

Find the equation of the tangent to the circle x2 + y2 = 16 drawn from the point (1, 4).

Q10

Find the equation of the normal to the circle x2 + y2 = 2x, which is parallel to the line x + 2y = 3.