Question

Consider an ellipse with foci at $(5,15)$ and $(21,15)$. If the x-axis is a tangent to the ellipse, then the length of its major axis equals?

• A. $17$
• B. $34$
• C. $13$
• D. $\sqrt{416}$

Answer 1

The correct option is B $34$

Centre of ellipse $=\frac{21+5}{2},\frac{15+15}{2}$

$=(13,15)$

$\therefore$ x-axis touches ellipse at $(13,0)\Rightarrow 2b=30$

$\Rightarrow b=15$

Now, $b^2=a^2-a^2{c}^2$

$\Rightarrow ac=\left|2\right|-\left|3\right|=\left|5\right|-\left|3\right|$

$=8$

$\therefore {15}^2=a^2-8^2$

$\Rightarrow a^2=25+64$

$=289$

$\Rightarrow a=17$

$\Rightarrow 2a=24$

Hence, the answer is $34.$