JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
If the normal at an end of a latus rectum of an ellipse passes through an extremity of the minor axis, then the eccentricity \(e\) of the ellipse satisfies
- A \(e ^{2}+2 e -1=0\)
- B \(e ^{2}+ e -1=0\)
- C \(e ^{4}+2 e ^{2}-1=0\)
- D \(e ^{4}+ e ^{2}-1=0\)
Answer & Solution
Correct Answer
(D) \(e ^{4}+ e ^{2}-1=0\)
Step-by-step Solution
Detailed explanation
\(\frac{ a ^{2} x }{ x _{1}}-\frac{ b ^{2} y }{ y _{1}}= a ^{2} e ^{2}\) \(\frac{a^{2} x}{a e}-\frac{b^{2} y}{b^{2}} \cdot a=a^{2} e^{2}\) \(\frac{ ax }{ e }- ay = a ^{2} e ^{2} \Rightarrow \frac{ x }{ e }- y = ae ^{2}\) passes through \((0,\) b)…
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