JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let \( (h, k) \) lie on the circle \( C: x^{2}+y^{2}=4 \) and the point \( (2h+1, 3k+2) \) lie on an ellipse with eccentricity \( e \). Then the value of \( \frac{5}{e^{2}} \) is equal to ___ .
- A 5
- B 7
- C 9
- D 11
Answer & Solution
Correct Answer
(C) 9
Step-by-step Solution
Detailed explanation
Let \(P \equiv(2 \cos \theta, 2 \sin \theta)\) ∴ coordinates of \(Q=(4 \cos \theta+1,6 \sin \theta+3)\) ∴ locus of \(Q\) is \(\left(\frac{x-1}{4}\right)^2+\left(\frac{y-3}{6}\right)^2=1\) \(\therefore e ^2=1-\frac{16}{36}=\frac{5}{9}\) \(\therefore \frac{5}{ e ^2}=9\)
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