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  4. If the circle x2 + y2 - 6x - 8y + (25 - a2) = 0 touches the axis of x, then a equals.

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Q. If the circle $x^2 + y^2 - 6x - 8y + (25 - a^2) = 0$ touches the axis of $x$, then a equals.

JEE MainJEE Main 2013Conic Sections

Solution:

$x^{2}+y^{2}-6x+8y+\left(25-a^{2}\right)=0$
Radius $=4\sqrt{9+16+\left(25-a^{2}\right)}$
$\Rightarrow a=\pm4$

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