Question

Equation of the pair of tangents from $(3,4)$ to the ellipse $\frac{x^2}{9}+\frac{y^2}{16}=1$ is:

• A. $(x+3)(y+4)=xy$
• B. $(x-3)(y-4)=xy$
• C. $(x+4)(y+3)=xy$
• D. $(x-4)(y-3)=xy$

Answer 1

Answer: (B)

$(x-3)(y-4)=xy$

Equation of the tangent to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ at the point $(x_1,y_1)$ is given by :

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

Therefore tangent to the ellipse $\frac{x^2}{9}+\frac{y^2}{16}=1$ at $(3,4)$ is given by :

$\frac{3x}{9}+\frac{4y}{16}=1$

$\Rightarrow$ $\frac{x}{3}+\frac{y}{4}=1$

$\Rightarrow$ $4x+3y-12=0$

$\Rightarrow$ $(x-3)(y-4)=xy$