If \(x^2+y^2+6 x+2 k y+25=0\) to touch \(Y\)-axis, then \(k=\)

If \(x^2+y^2+6 x+2 k y+25=0\) to touch \(Y\)-axis, then \(k=\)
  1. \pm 20
  2. \(-1,-5\)
  3. \pm 5
  4. 4

Solution

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 \(=\sqrt{9+k^2-25}\) \(\Rightarrow \sqrt{k^2-16}=3 \Rightarrow k^2=25 \Rightarrow k= \pm 5\)

Asked in: AP EAMCET 2020 (17 Sep Shift 1)

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