Circle(s) touching -axis at a distance 3 from the origin and having an intercept of length on -axis is (are) [2013]

Question

Circle(s) touching $x$ -axis at a distance 3 from the origin and having an intercept of length $2 \sqrt{7}$ on $y$ -axis is (are) [2013]

Smart Achievers · Accepted Answer

(1, 3)

Here, there are two possibilities for the given circle as shown in the figure.

$∴$ $The equations of circles can be$

${(x - 3)}^{2} + {(y - 4)}^{2} = 4^{2} or {(x - 3)}^{2} + {(y + 4)}^{2} = 4^{2}$

$\Rightarrow x^{2} + y^{2} - 6 x - 8 y + 9 = 0 or x^{2} + y^{2} - 6 x + 8 y + 9 = 0$

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