Question

Equation of the tangent and the normal drawn at the point $(6,0)$ on the ellipse $\frac{x^2}{36}+\frac{y^2}{9}=1$ respectively are

• A. $x=6$, $y=0$
• B. $y+x-6=0$, $y-x+6=0$
• C. $x=0$, $y=3$
• D. $x=-6$, $y=0$

Answer 1

The correct option is A $x=6$, $y=0$

Solution:

Equation of the ellipse :$\frac{x^2}{36}+\frac{y^2}{9}=1$

Equation of the tangent at $(x_1,y_1)$ is

$\frac{x{x}_1}{36}+\frac{y{y}_1}{9}=1$

$\therefore$ at $(6,0)$

$\frac{6x}{36}+\frac{y\times 0}{9}=1$

$⟹\frac{x}{6}=1$

$⟹x=6$ is the equation of the tangent passing through $(6,0).$

Tangents and normal are perpendicular to each-other.

$\therefore y=0$ is the equation of the normal passing through $(6,0).$

Hence, A is the correct option.