QJEEM19Ma90dd: JEE Main 2019 Mathematics - Class 12 JEEM19Ma90dd Solution: If the area enclosed between the curves y = kx 2 and x = ky 2 , …

Question

Verified Solution • 2025–26 Session moderate

If the area enclosed between the curves y = kx² and x = ky², (k > 0), is 1 square unit. Then k is -

Accepted Answer

Area bounded by

y² = 4ax & x² = 4by, a, b

\neq

0

is

| \frac{16 a b}{3} |

by using formula :

4a

=

\frac{1}{k} = 4 b, k > 0

Area

= | \frac{16. \frac{1}{4 k} . \frac{1}{4 k}}{3} | = 1

\Rightarrow

k²

= \frac{1}{3}

\Rightarrow

k

= \frac{1}{\sqrt{3}}

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