The length of the latus rectum of the ellipse 9x2 + 16y2 = 144 is

Question

The length of the latus rectum of the ellipse 9x2 + 16y2 = 144 is (A) 4 (B) 11/4 (C) 7/2 (D) 9/2

Tardigrade Admin · Accepted Answer

Given equation of ellipse is 9x2 + 16 y2= 144 or (9/144)x2+(16/144) y2=1 or (x2/(4)2)+(y2/(3)2)=1 ∴ a=4, b=3. Length of latus rectum =(2b2/a)=(2⋅ 9/4)=(9/2)

Q. The length of the latus rectum of the ellipse $9 x^{2} + 16 y^{2} = 144$ is

$4$

$11/4$

$7/2$

$9/2$

Given equation of ellipse is $9 x^{2} + 16 y^{2} = 144$
or $\frac{9}{144} x^{2} + \frac{16}{144} y^{2} = 1$
or $\frac{x ^{2}}{( 4 ) ^{2}} + \frac{y ^{2}}{( 3 ) ^{2}} = 1$
$∴ a = 4$ , $b = 3$ .
Length of latus rectum $= \frac{2 b ^{2}}{a} = \frac{2 \cdot 9}{4} = \frac{9}{2}$

Q. The length of the latus rectum of the ellipse 9x2+16y2=144 is

4

11/4

7/2

9/2

Given equation of ellipse is 9x2+16y2=144 or 1449​x2+14416​y2=1 or (4)2x2​+(3)2y2​=1 ∴a=4, b=3. Length of latus rectum =a2b2​=42⋅9​=29​

Q. The length of the latus rectum of the ellipse $9 x^{2} + 16 y^{2} = 144$ is

$4$

$11/4$

$7/2$

$9/2$

Given equation of ellipse is $9 x^{2} + 16 y^{2} = 144$
or $\frac{9}{144} x^{2} + \frac{16}{144} y^{2} = 1$
or $\frac{x ^{2}}{( 4 ) ^{2}} + \frac{y ^{2}}{( 3 ) ^{2}} = 1$
$∴ a = 4$ , $b = 3$ .
Length of latus rectum $= \frac{2 b ^{2}}{a} = \frac{2 \cdot 9}{4} = \frac{9}{2}$