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  4. The locus of centre of circle which touches the circle x2+y2-8 x-8 y+23=0 and the y-axis is a conic whose latus rectum is

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Q. The locus of centre of circle which touches the circle $x^2+y^2-8 x-8 y+23=0$ and the $y$-axis is a conic whose latus rectum is

Conic Sections

Solution:

$r=\sqrt{4^2+4^2-23}=3$
Locus of centre is a parabola with focus $(4,4)$ and directrix $x=-3$

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