Question

If any tangent to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ makes equal intercepts of length $l$ on the axes then $l=$

• A. $a^2+b^2$
• B. $\sqrt{a^2+b^2}$
• C. $(a^2+b^2{)}^2$
• D. $a+b$

Answer 1

The correct option is B $\sqrt{a^2+b^2}$

lf any tangent to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ makes equal intercepts of length $l$ on the axes then equation of tangent is $x+y=l$
where, $m=-1$ and $c=l$
We know that $c=\sqrt{a^2{m}^2+b^2}$
Therefore, $l=\sqrt{a^2+b^2}$