Question

Let P (4, 3) be a point on the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}} = 1.$ If the normal at P intersects the X-axis at (16, 0), then the eccentricity of the hyperbola is

• A. $\frac{\sqrt{5}}{2}$
• B. $2$
• C. $\sqrt{2}$
• D. $\sqrt{3}$

Answer 1

Answer: (B)

$2$

Answer 2

Normal at P(4, 3)
$\frac{a^{2}x}{4} + \frac{b^{2}y}{3} = a^{2}+b^{2}$ through (16, 0)
$\Rightarrow 4a^{2} = a^{2} + b^{2}$
$\Rightarrow \frac{b^{2}}{a^{2}} = 3\,\therefore\, e = 2$