JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
If the ellipse \(\frac{ x ^{2}}{ a ^{2}}+\frac{ y ^{2}}{ b ^{2}}=1\) meets the line \(\frac{x}{7}+\frac{y}{2 \sqrt{6}}=1\) on the \(x\)-axis and the line \(\frac{x}{7}-\frac{y}{2 \sqrt{6}}=1\) on the \(y\)-axis, then the eccentricity of the ellipse is
- A \(\frac{5}{7}\)
- B \(\frac{2 \sqrt{6}}{7}\)
- C \(\frac{3}{7}\)
- D \(\frac{2 \sqrt{5}}{7}\)
Answer & Solution
Correct Answer
(A) \(\frac{5}{7}\)
Step-by-step Solution
Detailed explanation
\(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\) meets the line \(\frac{x}{7}+\frac{y}{2 \sqrt{6}}=1\) on the \(x\)-axis So, \(a=7\) and \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\) meets the line \(\frac{x}{7}-\frac{y}{2 \sqrt{6}}=1\) on the \(y\)-axis So, \(b=2 \sqrt{6}\)…
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