Find the length of latus rectum of the parabola y2 = 8x.

Question

Find the length of latus rectum of the parabola y2 = 8x. (A) 8 (B) 4 (C) 16 (D) 2

Tardigrade Admin · Accepted Answer

The given parabola is, y 2+8 x -2 y +17=0 beginarrayl ⇒( y 2-2 y +1)=-8 x -17+1=-8 x -16 ⇒( y -1)2=-8( x +2) endarray Comparing with standard parabola Y 2=-4 a X Y = y -1, X = x +2, a =2 Hence length of latus rectum is =4 a=4 × 2=8

Q. Find the length of latus rectum of the parabola $y^{2} = 8 x$ .

$8$

$4$

$16$

$2$

Q. Find the length of latus rectum of the parabola y2=8x.

8

4

16

2

The given parabola is, y2+8x−2y+17=0 <br/><br/>⇒(y2−2y+1)=−8x−17+1=−8x−16<br/>⇒(y−1)2=−8(x+2)<br/>​<br/> Comparing with standard parabola Y2=−4aX <br/>Y=y−1,X=x+2,a=2<br/> Hence length of latus rectum is =4a=4×2=8

Q. Find the length of latus rectum of the parabola $y^{2} = 8 x$ .

$8$

$4$

$16$

$2$