Question:medium
Given point \( P(6, 4\sqrt{5}) \) satisfies the hyperbola
\[
\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1
\]
where eccentricity is a root of the equation \( 9e^2 - 21e + 10 = 0 \).
Then find the length of latus rectum of the hyperbola
\[
\frac{x^2}{a^2} - \frac{y^2}{2(1+b^2)} = 1.
\]
Given point \( P(6, 4\sqrt{5}) \) satisfies the hyperbola
\[
\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1
\]
where eccentricity is a root of the equation \( 9e^2 - 21e + 10 = 0 \).
Then find the length of latus rectum of the hyperbola
\[
\frac{x^2}{a^2} - \frac{y^2}{2(1+b^2)} = 1.
\]
Updated On: Apr 7, 2026
- \( \frac{56}{3} \)
- \( \frac{68}{3} \)
- \( \frac{52}{3} \)
- \( \frac{70}{3} \)
Show Solution
The Correct Option is B
Solution and Explanation
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