Question

The equations of the tangnets to the ellipse $4x^2+3y^2=5$ which are perpendicular to the line $3x-y+7=0$ are :

• A. $2x-2y\pm \sqrt{55}=0$
• B. $2x+2y\pm \sqrt{55}=0$
• C. $2x+6y\pm \sqrt{65}=0$
• D. $2x+2y\pm \sqrt{15}=0$

Answer 1

The correct option is C $2x+6y\pm \sqrt{65}=0$

Slope of the tangents $=-\frac{1}{3}$
and for the given ellipse $a^2=\frac{5}{4},b^2=\frac{5}{3}$
Equation of tangent in slope from is :
$y=mx\pm \sqrt{a^2{m}^2+b^2}$
$\Rightarrow y=-\frac{1}{3}x\pm \sqrt{\frac{5}{4}\times \frac{1}{3^2}+\frac{5}{3}}$
$\therefore 6y+2x\pm \sqrt{65}=0$