Physics, asked by paavanchirithoti, 7 months ago

One end of latusrectum of the parabola is

Answers

Answered by SɴᴏᴡʏSᴇᴄʀᴇᴛ
8

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Given equation is y2−4x−2y−3=0

⇒({y}^2 −2y)=4x+3

{(y-1)}^2 −1=4x+3

({y-1)}^2 =4(x+1)

Shift the origin to (−1,1)

{y}^2 =4X

Here focus is at (1,0).

Hence, focus of original parabola becomes

(1−1,0+1)=(0,1)

Therefore, equation of latusrectum is x=0.

Thus,

Point of intersection of parabola and latus rectum is,

{y}^2 −2y−3=0

⇒ y = −1 or 3

So, the required points are (0,−1),(0,3).

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