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JEE Mains · Maths · STD 12 - 6. Application of derivatives
Let \(x=4\) be a directrix to an ellipse whose centre is at the origin and its eccentricity is \(\frac{1}{2}\) If \(P (1, \beta), \beta>0\) is a point on this ellipse, then the equation of the normal to it at \(P\) is
- A \(7 x-4 y=1\)
- B \(4 x-2 y=1\)
- C \(4 x-3 y=2\)
- D \(8 x-2 y=5\)
Answer & Solution
Correct Answer
(B) \(4 x-2 y=1\)
Step-by-step Solution
Detailed explanation
Ellipse \(: \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\) directrix \(: x=\frac{a}{e}=4 \quad \& e =\frac{1}{2}\) \(\Rightarrow a =2 \& b ^{2}= a ^{2}\left(1- e ^{2}\right)=3\) \(\Rightarrow \quad\) Ellipse is \(\frac{ x ^{2}}{4}+\frac{ y ^{2}}{3}=1\) \(P\) is…
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