Question

Find the equation of the tangents to the ellipse $9x^2+16y^2=144$ which are parallel to the line $x+3y+k=0$

• A. $3y+x\pm \sqrt{97}=0$
• B. $3y-x\pm \sqrt{97}=0$
• C. $-3y-x\pm \sqrt{97}=0$
• D. $-3y+x\pm \sqrt{97}=0$

Answer 1

Answer: (A), (C)

$3y+x\pm \sqrt{97}=0$
$-3y-x\pm \sqrt{97}=0$

Equation of tangent is $y=mx\pm \sqrt{a^2{m}^2+b^2}$
Where, $m=-\frac{1}{3}$
Therefore, $y=\frac{-x}{3}\pm \sqrt{\frac{16}{9}+9}$
$\Rightarrow 3y+x\pm \sqrt{97}=0$