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If curve y = 1 - ax^2 and y = x^2 inters...

If curve `y = 1 - ax^2 and y = x^2` intersect orthogonally then the value of a is

A

`1/2`

B

`1/3`

C

`2`

D

`3`

Text Solution

Verified by Experts

The correct Answer is:
B
`y=1-ax^(2)implies(dy)/(dx)=-2ax`
`y=x^(2)implies(dy)/(dx)=2x`
two curves intersect orthogonally if
`(-2ax)(2x)=-1`
`implies4ax^(2)=1`……..i
from equation of curve
`1-ax^(2)=x^(2)`
`impliesx^(2)=1/(1+a)`………ii
from i and ii
`(4a)/(1+a)=1`
`impliesa=1/3`
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