Question

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

List I	List II
(i) The equation of the major axis	(a) $3x=34$
(ii) The equation of a directrix	(b)=2y
(iii) The equation of a latus rectum	(c) $x+y=9$
	(d) $x=6$
	(e) $x=3$
	(f) $3y=34$

The correct matching is

• A. (i)- (e); (ii)- (a); (iii)- (d)
• B. (i)- (b); (ii)- (f); (iii)- (e)
• C. (i)- (b); (ii)- (a); (iii)- (e)
• D. (i)- (b); (ii)- (e); (iii)- (d)

Answer 1

The correct option is A (i)- (e); (ii)- (a); (iii)- (d)

equation of ellipse is $\frac{(x-3{)}^2}{5^2}+\frac{(y-2{)}^2}{4^2}=1$
it is clear that equation of Major Axis $\Rightarrow x=3$
because $25>16$ and at it is passing through the center
$e=\frac{\sqrt{25-16}}{5}=\frac{3}{5}$
equation of directrix $\Rightarrow x=3+\frac{5}{\frac{3}{5}}=\frac{34}{3}\Rightarrow 3x=34$
x coordinate of Focus $=3+5\times \frac{3}{5}=6$
and Latus Rectum which passes through the Focus it must have the Equation $x=6$
Therefore Answer is $A$