Question

If $l_1$ is the tangent to $2x^2+3y^2=35$ at $(4,-1)$ and $l_2$ is the tangent to $4x^2+y^2=25$ at $(2,-3),$ then distance between $l_1$ and $l_2$ is :

• A. $\frac{10}{\sqrt{73}}$ unit
• B. $\frac{60}{\sqrt{73}}$ unit
• C. $\frac{25}{3\sqrt{2}}$ unit
• D. $\frac{5}{3\sqrt{2}}$ unit

Answer 1

The correct option is A $\frac{10}{\sqrt{73}}$ unit

Tangent at point $(4,-1)$ to ellipse $2x^2+3y^2=35$ is :
$l_1\equiv 8x-3y=35$
Tangent at point $(2,-3)$ to ellipse $4x^2+y^2=25$ is:
$l_2\equiv 8x-3y=25$
These two are parallel lines,
$\therefore$ Distance between parallel lines is:
$=\left|\frac{35-25}{\sqrt{8^2+3^2}}\right|=\frac{10}{\sqrt{73}}$unit