NDA 2017 Maths · Mathematics · Conic Sections · medium

The length of the latus rectum of the parabola y^2=-8x is 8. 2. The foci of the ellipse (x^2/(16)+(y^2/(25)=1 lie on the y-axis.

Single correct option

Consider the following statements:
1. The length of the latus rectum of the parabola

y^2=-8x

8

.
2. The foci of the ellipse

\frac{x^2}{16}+\frac{y^2}{25}=1

lie on the

y

-axis.
Which of the statements given above is/are correct?

Show answer and solution

Answer: (C) Both $1$ and $2$

1: the latus rectum of

y^2=-4ax

has length

4a=8

regardless of orientation. 2: the larger denominator

25

is under

y^2

, so the major axis is along the

y

-axis and the foci are

(0,\pm3)

. Both are correct; the common error is to assume the foci are always on the

x

-axis.

Original question written in the NDA 2017 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake