Question

The equation of the tangents to the ellipse $3x^2+4y^2=12$ which are parallel to the line $2x-y+5=0$ are

• A. $6x-2y\pm \sqrt{\frac{155}{3}}=0$
• B. $2x-y\pm \sqrt{19}=0$
• C. $16x+22y\pm \sqrt{\frac{155}{3}}=0$
• D. $2x+2y\pm \sqrt{39}=0$

Answer 1

The correct option is B $2x-y\pm \sqrt{19}=0$

Given, ellipse $3x^2+4y^2=12$
and line $2x-y+5=0$
slope is $m=2$
Required tangents to the ellipse $3x^2+4y^2=12$ will be of form
$y=mx\pm \sqrt{4m^2+3}$
$\Rightarrow y=2x\pm \sqrt{4\left(2^2\right)+3}\Rightarrow y=2x\pm \sqrt{19}$