Let a and b respectively be the semi-transverse and semi-conjugate axes of a standard hyperbola whose eccentricity satisfies the equation…

Question

Let a and b respectively be the semi-transverse and semi-conjugate axes of a standard hyperbola whose eccentricity satisfies the equation 9e^2-18e+5=0. If S5, 0 is a focus and 5x=9 is the corresponding directrix of this hyperbola, then a^2-b^2 is equal to

MARKS Content Team · Accepted Answer

Correct answer: (A) -7. Given that focus of hyperbola is S5, 0 ⇒ae=5......i Therefore, Directrix x=a/e ⇒ a/e=9/5 ......ii From i and ii, we get ⇒ a^2=9 ⇒a=3 and e=5/3 (It satisfies 9e^2-18e+5=0 ) We also know that for an ellipse, b^2=a^2e^2-1 ⇒b^2=16 ⇒ a^2-b^2=9-16= -7

Let $a$ and $b$ respectively be the semi-transverse and semi-conjugate axes of a standard hyperbola whose eccentricity satisfies the equation $9 e^{2} - 18 e + 5 = 0$ . If $S (5, 0)$ is a focus and $5 x = 9$ is the corresponding directrix of this hyperbola, then $a^{2} - b^{2}$ is equal to

Solution

Relevant Questions

Let a and b respectively be the semi-transverse and semi-conjugate axes of a standard hyperbola whose eccentricity satisfies the equation 9e2-18e+5=0. If S5, 0 is a focus and 5x=9 is the corresponding directrix of this hyperbola, then a2-b2 is equal to

Solution

Relevant Questions

Let $a$ and $b$ respectively be the semi-transverse and semi-conjugate axes of a standard hyperbola whose eccentricity satisfies the equation $9 e^{2} - 18 e + 5 = 0$ . If $S (5, 0)$ is a focus and $5 x = 9$ is the corresponding directrix of this hyperbola, then $a^{2} - b^{2}$ is equal to