If the line x - 2y = 12 is tangent to the ellipse (x2/a2) + (y2/b2) = 1 at the point ( 3, (-9/2) ), then the length of the latus recturm of the ellipse is :

Question

If the line x - 2y = 12 is tangent to the ellipse (x2/a2) + (y2/b2) = 1 at the point ( 3, (-9/2) ), then the length of the latus recturm of the ellipse is : (A) 9 (B)  8 √3 (C)  12 √2 (D) 5

Tardigrade Admin · Accepted Answer

Tangent at (3, - (9/2)) (3x/a2) - (9y/2b2) = 1 Comparing this with x - 2y = 12 (3/a2 ) = (9/4b2) = (1/12) we get a = 6 and b = 3 √3 L(LR)= ( 2b2/a) = 9

Q. If the line $x - 2 y = 12$ is tangent to the ellipse $\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1$ at the point $(3, \frac{- 9}{2})$ , then the length of the latus recturm of the ellipse is :

$9$

$83$

$122$

$5$

Tangent at $(3, - \frac{9}{2})$
$\frac{3 x}{a ^{2}} - \frac{9 y}{2 b ^{2}} = 1$
Comparing this with $x - 2 y = 12$
$\frac{3}{a ^{2}} = \frac{9}{4 b ^{2}} = \frac{1}{12}$
we get a = 6 and b = $33$ $L (L R) = \frac{2 b ^{2}}{a} = 9$

Q. If the line x−2y=12 is tangent to the ellipse a2x2​+b2y2​=1 at the point (3,2−9​), then the length of the latus recturm of the ellipse is :

9

83​

122​

5

Tangent at (3,−29​) a23x​−2b29y​=1 Comparing this with x−2y=12 a23​=4b29​=121​ we get a = 6 and b = 33​ L(LR)=a2b2​=9

Q. If the line $x - 2 y = 12$ is tangent to the ellipse $\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1$ at the point $(3, \frac{- 9}{2})$ , then the length of the latus recturm of the ellipse is :

$9$

$83$

$122$

$5$

Tangent at $(3, - \frac{9}{2})$
$\frac{3 x}{a ^{2}} - \frac{9 y}{2 b ^{2}} = 1$
Comparing this with $x - 2 y = 12$
$\frac{3}{a ^{2}} = \frac{9}{4 b ^{2}} = \frac{1}{12}$
we get a = 6 and b = $33$ $L (L R) = \frac{2 b ^{2}}{a} = 9$