Question

For the ellipse given $\frac{{(x-3)}^2}{25}+\frac{{(y-2)}^2}{16}=1$, match the equations of the lines given in List $I$ and List $II$.

List $I$	List $II$
$\left(i\right)$ The equation of the major axis	$\left(a\right)$ $3x=34$
$\left(ii\right)$ The equation of a directirix	$\left(b\right)$ $y=2$
$\left(iii\right)$ The equation of a latus rectum	$\left(c\right)$$x+y=0$
	$\left(d\right)$ $x=6$
	$\left(e\right)$ $x=3$
	$\left(f\right)$ $3y=34$

• A. $\left(i\right)\to e,\left(ii\right)\to a,\left(iii\right)\to d$
• B. $\left(i\right)\to b,\left(ii\right)\to f,\left(iii\right)\to e$
• C. $\left(i\right)\to b,\left(ii\right)\to a,\left(iii\right)\to e$
  
• D. $\left(i\right)\to b,\left(ii\right)\to a,\left(iii\right)\to d$
  

Answer 1

The correct option is D $\left(i\right)\to b,\left(ii\right)\to a,\left(iii\right)\to d$

Given equation of ellipse is $\frac{(x-3{)}^2}{25}+\frac{(y-2{)}^2}{16}=1$

Thus, we have $h=3,k=2,a=5,b=4$
Major axis $\Rightarrow$ $y-k=0$ $\Rightarrow$ $y-2=0$
Directrix $\Rightarrow$ $x=h+\frac{a}{e}=3+\frac{5}{\frac{3}{5}}$
$\Rightarrow 3x=34$
Latus rectum $\Rightarrow$ $x=h+ae$
$\Rightarrow x=3+5\times \frac{3}{5}$
$\Rightarrow x=6$