Practicing Success
The point on the curve $y^2=x$ where tangent makes 45° angle with x-axis, is |
(1/2, 1/4) (1/4, 1/2) (4, 2) (1, 1) |
(1/4, 1/2) |
Let $\left(x_1, y_1\right)$ be the required point on the curve $y^2=x$. Then, $\left(\frac{d y}{d x}\right)_{\left(x_1, y_1\right)}=1$ $\Rightarrow \frac{1}{2 y_1}=1$ $\left[∵ y^2=x \Rightarrow 2 y \frac{d y}{d x}=1 \Rightarrow \frac{d y}{d x}=\frac{1}{2 y}\right]$ $\Rightarrow y_1=\frac{1}{2}$ Since $\left(x_1, y_1\right)$ lies on $y^2=x$. ∴ $x_1=y_1{ }^2 \Rightarrow x_1=\frac{1}{4}$ Hence, (1/4, 1/2) is the required point. |