The line which is parallel to X-axis and crosses the curve y = √x at an angle of 45°, is

Question

The line which is parallel to X-axis and crosses the curve y = √x at an angle of 45°, is (A) x = (1/4) (B) y = (1/4) (C) y = (1/2) (D) y = 1

Tardigrade Admin · Accepted Answer

Let the line parallel to x axis be y=k.So,the point of intersection of the line and the curve will be ( k 2, k ). The slope of the curve at any point ( x , y ) is ( partial y / partial x )= (1/2 √x)=(1/2 k)=1 Hence k=1 / 2

Q. The line which is parallel to X-axis and crosses the curve $y = x$ at an angle of $4 5^{\circ}$ , is

$x = \frac{1}{4}$

$y = \frac{1}{4}$

$y = \frac{1}{2}$

y = 1

Let the line parallel to $x$ axis be $y = k$ .So,the point of intersection of the line and the curve will be $(k^{2}, k)$ . The slope of the curve at any point $(x, y)$ is $\frac{\partial y}{\partial x} =$ $\frac{1}{2 x} = \frac{1}{2 k} = 1$
Hence $k = 1/2$

Q. The line which is parallel to X-axis and crosses the curve y=x​ at an angle of 45∘, is

x=41​

y=41​

y=21​