A) \[(4,\,4)\]
B) \[(4,\,\,-\,4)\]
C) \[(-4,\,\,4)\]
D) \[(-4,\,\,-4)\]
Correct Answer: A
Solution :
Given, \[{{y}^{2}}=4x\] On differentiating w.r.t. x, we get \[2y\frac{dy}{dx}=4\] \[\Rightarrow \] \[\frac{dy}{dx}=\frac{2}{y}\] Since, the tangent to the curve is perpendicular to the line \[2x+y=-2\] \[\therefore \] \[\frac{2}{y}\times (-2)=-1\] \[(\because \,\,\,{{m}_{1}}{{m}_{2}}=-1)\] \[\Rightarrow \] \[y=4\] \[\therefore \] From Eq. (i), \[{{(4)}^{2}}=4x\,\Rightarrow x=4\] Hence, required point is \[(4,4)\].
You need to login to perform this action.
You will be redirected in
3 sec
