NIMCET 2015 — Mathematics PYQ

1. Find the properties of the Ellipse:

The given equation is $\frac{x^2}{16}+\frac{y^2}{9}=1$.

Comparing this with the standard form $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$:

• $a^2=16⟹a=4$

• $b^2=9⟹b=3$

Since a > b, the major axis is along the X-axis.

2. Calculate the Eccentricity ($e$):

The relationship between $a$, $b$, and $e$ is:

3. Find the Foci of the Ellipse:

The coordinates of the foci are $(\pm ae,0)$:

So, the foci are $S(\sqrt{7},0)$ and $S^{\prime }(-\sqrt{7},0)$.

4. Find the Radius of the Circle:

The circle has its centre at $C(0,3)$ and passes through the foci $(\pm \sqrt{7},0)$.

The radius ($R$) is the distance between the centre $(0,3)$ and one of the foci $(\sqrt{7},0)$.

Using the distance formula:

Correct Option:

(a) $4$ units