Question

The length of the tangent from the point $(14,12)$ to the ellipse $\frac{x^2}{4}+\frac{y^2}{9}=1$ is

• A. $\frac{59}{\sqrt{1}7}$
• B. $\sqrt{1}3$
• C. $10$
• D. $8$

Answer 1

Answer: (A)

$\frac{59}{\sqrt{1}7}$

Equation of ellipse,

$\frac{x^2}{4}+\frac{y^2}{9}=1$

Point, $(14,12)$

Equation of a tangent is given by,

$\frac{x{x}_1}{a^2}+\frac{y{y}_1}{b^2}=1$

$\frac{x\left(14\right)}{2^2}+\frac{y\left(12\right)}{3^2}=1$

$\frac{x\left(7\right)}{2}+\frac{y\left(4\right)}{3}=1$

$2x+8y=6$

Using length formula, we calculate the length of tangent $2x+8y=6$

Distance $=\frac{2\times 14+8\times 12-6}{\sqrt{6}8}$

$=\frac{59}{\sqrt{1}7}$