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If the curves ay+x^2=7 and x^3=y cut ort...

If the curves `ay+x^2=7` and `x^3=y` cut orthogonally at `(1, 1)` then `a=` (A) 1 (B) `-6` (C) 6 (D) `1/6`

A

1

B

0

C

`-6`

D

6

Text Solution

Verified by Experts

The correct Answer is:
D
We have, `ay=x^(2)=7 "and" x^(3)=y`
On differentiating w.r.t. x in both equations, we get
`a.(dy)/(dx)+2x=0` and `3x^(2)=(dy)/(dx)`
`rArr (dy)/(dx)_(1,1)=-2/a=m_(1)`
and `(dy)/(dx)_(1,1)=3.1=3=m_(2)`
Since, the curves cut orthogonally at (1,1).
`therefore m_(1).m_(2)=-1`
`rArr (-2/a).3=-1`
`therefore a=6`
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