Question

The length of the tangent from the point $(3,-5)$ to the ellipse $4x^2+3y^2=12$, is given by

• A. $\frac{1}{2}\sqrt{17}$
• B. $\frac{1}{2}\sqrt{33}$
• C. $\frac{1}{2}\sqrt{37}$
• D. $\frac{1}{2}\sqrt{19}$

Answer 1

The correct option is B $\frac{1}{2}\sqrt{33}$

equation of ellipse

$4x^2+3y^2=12$

or $\frac{x^2}{3}+\frac{y^2}{4}=1$

or $\frac{x^2}{3}+\frac{y^2}{4}-1=0$

$\therefore S=\frac{x^2}{3}+\frac{y^2}{4}-1$

then length of tangent = $\sqrt{S_1}$

where $S_1=$ value of S ar $(x_1,y_1)$

$\therefore$ length = $\sqrt{\frac{3^2}{3}+\frac{(-5{)}^2}{4}-1}$

$=\sqrt{3+\frac{2S}{4}-1}$

$=\sqrt{\frac{\left(3.4\right)+2S-4}{4}}$

$=\sqrt{\frac{33}{4}}$

$=\frac{1}{2}\sqrt{33}$

wrong option