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  4. The equation of common normal to the circle x2+y2-12 x+16=0 and parabola y2=4 x is

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Q. The equation of common normal to the circle $x^2+y^2-12 x+16=0$ and parabola $y^2=4 x$ is

Conic Sections

Solution:

$ y=m x-2 a m-a m^3$
$ y=m x-2 m-m^3$
Passes through centre of circle
$ =6 m-2 m-m^3 \Rightarrow 4 m-m^3=0$
$ \Rightarrow m=0, m=2, m=-2$