Question

The abscissa of the focii of the ellipse $25(x^2-6x+9)+16y^2=400$ is:

• A. $(4,-ae),(4,ae)$
• B. $(3,-ae),(3,ae)$
• C. $(5,-ae),(5,ae)$
• D. None of these

Answer 1

The correct option is B $(3,-ae),(3,ae)$

The equation of the ellipse can be written as $\frac{(x-3{)}^2}{4^2}+\frac{y^2}{5^2}=1$
$\therefore$ Minor axis is along the line $x-3=0$ and major axis is $y=0$
$(\because a^2=4^2<b^2=5^2)$
$\therefore S$ and $S^{{}^{\prime }}$ are $(3,3),(3,-3)$
$\because 4^2=5^2(1-e^2)\Rightarrow e=\frac{3}{5}(\because ae=5\frac{3}{5}=3)$ and $S\equiv (3,ae)$, $S^{{}^{\prime }}\equiv (3,-ae).$
Ans: B