find equation of image of circle whose equation is x2+y2+8x-16y+64=0 in the line mirror x=0 - Maths - Conic Sections

Question

find equation of image of circle whose equation is
x2+y2+8x-16y+64=0 in the line mirror x=0

Gursheen kaur. · Accepted Answer

The equation of the given circle is $x^{2} + y^{2} + 8 x - 16 y + 64 = 0$

$\Rightarrow x^{2} + 8 x + 16 + (y^{2} - 16 y + 64) = 16 \Rightarrow {(x + 4)}^{2} + {(y - 8)}^{2} = 4^{2} \Rightarrow {[x - (- 4)]}^{2} + {(y - 8)}^{2} = 4^{2} t h u s, i t s c l e a r t h a t, i t s c e n t r e i n t h e l i n e m i r r o r h a s i t s c e n t r e (4, 8) a n d r a d i u s 4. s o, i t s {e q}^{n} i s {(x - 4)}^{2} + {(y - 8)}^{2} = 4^{2} \Rightarrow x^{2} + y^{2} - 8 x - 16 y + 64 = 0$