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Maths-

General

Easy

Question

For the ellipse $x squared over 4 plus y squared over 1 equals 1$ , the latus rectum is

$\frac{1}{2}$
1
2
4

hint Hint:

Latus rectum of ellipse is the focal chord that is perpendicular to the axis of the ellipse. The ellipse has two focus and hence there are two latus rectum for an ellipse. The length of the latus rectum of the ellipse having the standard equation of
$x squared over a squared plus y squared over b squared equals 1$ is $fraction numerator 2 b squared over denominator a end fraction$

The correct answer is: 1

Latus rectum of ellipse is the focal chord that is perpendicular to the axis of the ellipse. The ellipse has two focus and hence there are two latus rectum for an ellipse. The length of the latus rectum of the ellipse having the standard equation of
$x squared over a squared plus y squared over b squared equals 1$ is $fraction numerator 2 b squared over denominator a end fraction$
Given : $x squared over 4 plus y squared over 1 equals 1 space equals space x squared over 2 squared plus y squared over 1 squared comma space w h e r e space a squared space equals space 2 squared space a n d space b squared space equals 1$
Length of latus rectum = $fraction numerator 2 b squared over denominator a end fraction$ = $fraction numerator 2 space cross times space 1 over denominator 2 end fraction space equals space 1$
Thus, for the ellipse $fraction numerator x to the power of 2 end exponent over denominator 1 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 4 end fraction equals 1$ , the latus rectum is 1.

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