Question

An ellipse has its centre at $(1,-1)$ and semi major axis equal to $8$. If this ellipse passes through the point $(1,3)$, its eccentricity is equal to

• A. $\frac{1}{\sqrt{2}}$
• B. $\frac{1}{2}$
• C. $\frac{\sqrt{3}}{2}$
• D. none of these

Answer 1

The correct option is C $\frac{\sqrt{3}}{2}$

Shifting origin to $(1,-1)\Rightarrow x-1=x,y+1=y$

Now ellipse pass through $(0,4)$ and $a=8$

$\Rightarrow b=4\Rightarrow e^2=1-\frac{b^2}{a^2}=1-{\left(\frac{4}{8}\right)}^2=1-\frac{1}{4}=\frac{3}{4}$

$\Rightarrow e=\frac{\sqrt{3}}{2}$