Question

The tangent to the curve y² = 4x at (1, 2) is inclined to the x-axis at an angle of​

Answer 1

Answer:

$\frac{\pi }{4}$

Step-by-step explanation:

Finding the $\frac{dy}{dx}$ of the curve.

$\frac{dy}{dx}(y^2)=\frac{dy}{dx}(4x)$

⇒$2y\frac{dy}{dx}=4$

Substituting the point $(1,2)$ in above equation -

⇒$2(2)\frac{dy}{dx}=4$

⇒$4\frac{dy}{dx} =4$

⇒$\frac{dy}{dx}=1$

Now, Substituting $\frac{dy}{dx}$ by $tan\alpha$,

$tan\alpha =1$

$\alpha =tan^-^11$

$\alpha =\frac{\pi }{4}$