The length of the latus rectum of the parabola 169[(x-1)2+(y-3)2]=(5 x-12 y+ 17) 2 is:

Question

The length of the latus rectum of the parabola 169[(x-1)2+(y-3)2]=(5 x-12 y+ 17) 2 is: (A) (14/13) (B) (12/13) (C) (28/13) (D) None of these

Tardigrade Admin · Accepted Answer

Given equation can be rewritten as (x-1)2+(y-3)2=((5 x-12 y+17/13))2 ⇒ S P=P M Here, focus is (1,3), directrix 5 x-12 y+17=0 ∴ the distance of the focus from the directrix =|(5-36+17/√25+144)| =(14/13)=2 a ∴ Latusrectum =2 × (14/13)=(28/13)

Q. The length of the latus rectum of the parabola
$169 [(x - 1)^{2} + (y - 3)^{2}] = (5 x - 12 y + 17)^{2}$ is:

$\frac{14}{13}$

$\frac{12}{13}$

$\frac{28}{13}$

None of these

Q. The length of the latus rectum of the parabola 169[(x−1)2+(y−3)2]=(5x−12y+17)2 is:

1314​

1312​

1328​

None of these

Given equation can be rewritten as (x−1)2+(y−3)2=(135x−12y+17​)2 ⇒SP=PM Here, focus is (1,3), directrix 5x−12y+17=0 ∴ the distance of the focus from the directrix =∣∣​25+144​5−36+17​∣∣​ =1314​=2a ∴ Latusrectum =2×1314​=1328​

Q. The length of the latus rectum of the parabola
$169 [(x - 1)^{2} + (y - 3)^{2}] = (5 x - 12 y + 17)^{2}$ is:

$\frac{14}{13}$

$\frac{12}{13}$

$\frac{28}{13}$