JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let \(x = 9\) be a directrix of an ellipse \(E\), whose centre is at the origin and eccentricity is \(\dfrac{1}{3}\). Let \(P(\alpha, 0)\), \(\alpha > 0\), be a focus of \(E\) and \(AB\) be a chord passing through \(P\). Then the locus of the mid point of \(AB\) is :
- A \(9y^2 = 8x(1-x)\)
- B \(3y^2 = 4x(1-x)\)
- C \(9y^2 = 8x(x-1)\)
- D \(3y^2 = 4x(x-1)\)
Answer & Solution
Correct Answer
(A) \(9y^2 = 8x(1-x)\)
Step-by-step Solution
Detailed explanation
Given the directrix of the ellipse is \(x = \dfrac{a}{e} = 9\) and eccentricity \(e = \dfrac{1}{3}\). \(\dfrac{a}{1/3} = 9 \Rightarrow a = 3\) The value of \(b^2\) is given by \(b^2 = a^2(1 - e^2) = 9\left(1 - \dfrac{1}{9}\right) = 8\). The equation of the ellipse is…
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