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

Question

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 $$ \ne $$ 0

is $$\left| {{{16ab} \over 3}} \right|$$

by using formula :

4a $=$ $${1 \over k} = 4b,k > 0$$

Area $$ = \left| {{{16.{1 \over {4k}}.{1 \over {4k}}} \over 3}} \right| = 1$$

$$ \Rightarrow $$  k2 $$ = {1 \over 3}$$

$$ \Rightarrow $$  k $$ = {1 \over {\sqrt 3 }}$$

Solutions · 1