TS EAMCET · Maths · Ellipse
For \(k>0\), the shortest distance from a point \(P(1, k)\) on the ellipse \(9 x^2+4 y^2-18 x+16 y-11=0\) to one of its directrix is
- A \(3-\sqrt{5}\)
- B \(3+\sqrt{5}\)
- C \(\frac{9}{\sqrt{5}}-3\)
- D \(\frac{9}{\sqrt{5}}-2\)
Answer & Solution
Correct Answer
(C) \(\frac{9}{\sqrt{5}}-3\)
Step-by-step Solution
Detailed explanation
We, have, \(P(1, k)\) lies on ellipse \(\begin{aligned} & 9 x^2+4 y^2-18 x+16 y-11=0 \\ & \therefore \quad 9+4 k^2-18+16 k-11=0 \\ & \Rightarrow \quad 4 k^2+16 k-20=0 \\ & \Rightarrow \quad k^2+4 k-5=0 \\ & \Rightarrow \quad(k+5)(k-1)=0 \Rightarrow k=-5,1 \\ & \end{aligned}\)…
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