JEE Advanced · 2007 · 08 Apr 2007 · Paper 2 · Parabola

STATEMENT-1 : The curve

y = \frac{- x ^{2}}{2} + x + 1

is symmetric with respect to the line

x = 1

.

because

STATEMENT-2 : A parabola is symmetric about its axis.

(A)Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1✓ Correct
(B)Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(C)Statement-1 is True, Statement-2 is False
(D)Statement-1 is False, Statement-2 is True

Answer: (A)

Solution

Rewriting the equation:

y = - \frac{x ^{2}}{2} + x + 1 = - \frac{1}{2} (x^{2} - 2 x) + 1 = - \frac{1}{2} (x - 1)^{2} + \frac{3}{2}

This is in the form

y - k = a (x - h)^{2}

with vertex at

(1, \frac{3}{2})

.

The axis of symmetry is

x = 1

, so Statement-1 is TRUE.

Statement-2 is a general property of parabolas and is TRUE.

Since the curve is a parabola and Statement-2 explains why it is symmetric about

x = 1

, Statement-2 is a correct explanation for Statement-1.

JEE Advanced · 2007 · 08 Apr 2007 · Paper 2 · Single correct option

Practise more: all JEE Advanced PYQs on Parabola →

JEE Advanced · 2007 · 08 Apr 2007 · Paper 2 · Parabola

Solution

More JEE Advanced questions on Parabola