Question

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

Answer 1

The given circle and line are

x² + y²+ 16x – 24y + 183 = 0______(1) 

and 4x + 7y + 13 = 0______(2)

Centre and radius if the circle are 

(–8, 12) and \(\sqrt{64 + 144 – 183}\) = \(\sqrt{25}\) = 5 respectively.

Equation of line C₁C₂ is 7x – 4y + k = 0 it passes through (–8, 12)

∴ –56 – 48 + k = 0

k = 104

Equation of line C₁C₂ is 7x – 4y + 104 = 0______(3)

To get the coordinates of M. Solve the equation