# The Length of the Latus-rectum of the Parabola 4y2 + 2x − 20y + 17 = 0 is - Mathematics

MCQ

The length of the latus-rectum of the parabola 4y2 + 2x − 20y + 17 = 0 is

•  3

•  1/2

#### Solution

1/2

Given:
4y2 + 2x − 20y + 17 = 0

$\Rightarrow y^2 + \frac{x}{2} - 5y + \frac{17}{4} = 0$
$\Rightarrow \left( y - \frac{5}{2} \right)^2 + \frac{x}{2} - 2 = 0$
$\Rightarrow \left( y - \frac{5}{2} \right)^2 = - 1\left( \frac{x}{2} - 2 \right)$
$\Rightarrow \left( y - \frac{5}{2} \right)^2 = \frac{- 1}{2}\left( x - 4 \right)$

Let $X = x - 4, Y = y - \frac{5}{2}$

$\therefore Y^2 = \frac{- X}{2 ∴ Length of the latus rectum = 4a =∴ Length of the latus rectum = 4a =}$

$\frac{1}{2}$ units

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 25 Parabola
Q 18 | Page 30