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

Question

Let a and b respectively be the semitransverse and semi-conjugate axes of a hyperbola whose eccentricity satisfies the equation 9e2 -18e + 5 = 0. If S(5, 0) is a focus and 5x=9 is the corresponding directrix of this hyperbola, then a2 - b2 is equal to : (A) 7 (B) - 7 (C) 5 (D) -5

Tardigrade Admin · Accepted Answer

ae = 5 x=(9/5) ⇒ (a/e)=(9/5) ⇒ a2=9 (1) ⇒ e=(5/3) b2=a2(e2-1) ⇒ b2=16 a2-b2=9-16=-7

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

7

- 7

5

-5

ae $= 5$
$x = \frac{9}{5} \Rightarrow \frac{a}{e} = \frac{9}{5}$
$\Rightarrow a^{2} = 9$
$(1) \Rightarrow e = \frac{5}{3}$
$b^{2} = a^{2} (e^{2} - 1) \Rightarrow b^{2} = 16$
$a^{2} - b^{2} = 9 - 16 = - 7$

Q. Let a and b respectively be the semitransverse and semi-conjugate axes of a hyperbola whose eccentricity satisfies the equation 9e2−18e+5=0. If S(5, 0) is a focus and 5x=9 is the corresponding directrix of this hyperbola, then a2−b2 is equal to :

7

- 7

5

-5

ae =5 x=59​⇒ea​=59​ ⇒a2=9 (1)⇒e=35​ b2=a2(e2−1)⇒b2=16 a2−b2=9−16=−7

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

ae $= 5$
$x = \frac{9}{5} \Rightarrow \frac{a}{e} = \frac{9}{5}$
$\Rightarrow a^{2} = 9$
$(1) \Rightarrow e = \frac{5}{3}$
$b^{2} = a^{2} (e^{2} - 1) \Rightarrow b^{2} = 16$
$a^{2} - b^{2} = 9 - 16 = - 7$