If a hyperbola passes through the focus of the ellipse 25 x 2 + 16 y 2 = 1 and its transverse and conjugate axes coincides with the major and minor axes of the ellipse, and the product of eccentri

Question

If a hyperbola passes through the focus of the ellipse $\frac{x ^{2}}{25} + \frac{y ^{2}}{16} = 1$ and its transverse and conjugate axes coincides with the major and minor axes of the ellipse, and the product of eccentricities is 1 , represented by the equation $\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1$ , then the value of $b^{2} - a^{2}$ is

Answer:

7

Solution:

Using the hypothesis, we get equation to hyperbola as $\frac{x ^{2}}{9} - \frac{y ^{2}}{16} = 1 \Rightarrow b^{2} - a^{2} = 7$

TestHub · Accepted Answer

Using the hypothesis, we get equation to hyperbola as 9 x 2 ​ − 16 y 2 ​ = 1 ⇒ b 2 − a 2 = 7

Mathematics - Hyperbola Question with Solution | TestHub

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