Question

The equation of tangent to the ellipse $2x^2+3y^2=6$ which make an angle ${30}^O$ with the major axis is

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

Answer 1

The correct option is A $x-\sqrt{3}y\pm 3=0$

$2x^2+3y^2=6$

$\Rightarrow \frac{x^2}{3}+\frac{y^2}{2}=1$

$\Rightarrow a^2=3,b^2=2$

$\tan m={30}^{\circ }\Rightarrow m={\tan }^{-1}30=\frac{1}{\sqrt{3}}$

$y=mx+\sqrt{a^2{m}^2+b^2}$

$y=\left(\frac{1}{\sqrt{3}}\right)x+\sqrt{3{\left(\frac{1}{\sqrt{3}}\right)}^2+2}$

$\sqrt{3}y=x+\sqrt{3}\left(\sqrt{1+2}\right)$

$\sqrt{3}y=x\pm 3$

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