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If \(x^2+y^2+6 x+2 k y+25=0\) to touch \(Y\)-axis, then \(k=\)
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Verified Answer
The correct answer is:
\pm 5
Given circle
\(x^2+y^2+6 x+2 k y+25=0 \text { touches } Y \text {-axis }\)
and here centre is \((-3,-k)\) so radius \(=3\) units
Also radius \(=\sqrt{9+k^2-25}\)
\(\Rightarrow \sqrt{k^2-16}=3 \Rightarrow k^2=25 \Rightarrow k= \pm 5\)
\(x^2+y^2+6 x+2 k y+25=0 \text { touches } Y \text {-axis }\)
and here centre is \((-3,-k)\) so radius \(=3\) units
Also radius \(=\sqrt{9+k^2-25}\)
\(\Rightarrow \sqrt{k^2-16}=3 \Rightarrow k^2=25 \Rightarrow k= \pm 5\)
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