Question

Equation of the tangent of $\frac{x^2}{28}+\frac{y^2}{16}=1$ making an angle ${60}^{\circ }$ with $x$ -axis is:

• A. $y=\sqrt{3}x+5$
• B. $y=\sqrt{3}x+10$
• C. $y=\sqrt{3}x+7$
• D. $y=\sqrt{3}x+4$

Answer 1

The correct option is B $y=\sqrt{3}x+10$

Given, equation of tangent $\frac{x^2}{28}+\frac{y^2}{16}=1$

$y=mx+c$ represents a tangent with $c^2=a^2{m}^2+b^2$
Also given $m=\tan 60=\sqrt{3}$
$c^2=28\left(3\right)+16$
$=84+16$
$=100$
$\therefore c=10$
$\therefore y=\sqrt{3}x+10$