For the ellipse $\frac{x^{2}}{25} + \frac{y^{2}}{16} = 1$ , a list of lines given in List-I are to be matched with their equation given in List-II
List - I List - II
I) Directrix corresponding to the focus (–3,0) a) y = 4
ii) Tangent at the vertex (0,4) b) 3x=25
iii) Latus rectum through (3,0) c) x=3
d) y+4=0
e) x+3=0
f) 3x+25=0
The correct matching

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(i) (ii) (iii)

(b) (a) (e)

(i) (ii) (iii)

(f) (a) (c)

(i) (ii) (iii)

(b) (d) (c)

(i) (ii) (iii)

(f) (a) (e)

answer is B.

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Detailed Solution

$\frac{x^{2}}{25} + \frac{y^{2}}{16} = 1 a = 5 b = 4 e = \sqrt{\frac{25 - 16}{25}} = \frac{3}{5}$

i) equation of directrix is

$x = \frac{- 5}{(3 / 5)} = \frac{- 25}{3}$

ii) equation of Tangent at (0, 4) is y=4

iii) equation of L.R is x=ae $\Rightarrow$ x=3

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