Question

The measure of the angle of intersection between y²=x and x²=y other than one at (0,0) is.........,Select correct option from the given options.
(a) tan⁻¹4/3
(b) tan⁻¹3/4
(c) π/4
(d) π/2

Answer 1

There can be many ways, but as always, I'll go with the intuitive one.

Let's do some algebra,

x2−y2=0x2−y2=0

⟹x2=y2⟹x2=y2

⟹x=±⟹x=± yy

Or y=xy=x and y=−xy=−x are the two lines depicted by this conic.

We are familiar that they both are inclined at 45°45° with the axes, but on opposite sides, which also means that their slopes are equal but opposite in sign parity, which can be confirmed from the equations too.

Therefore, 45°+45°=90°45°+45°=90°

Or, because the product of the slopes is −1−1, therefore the lines are perpendicular to each other at the origin.

Hope that helped.

Answer 2

Answer:

π/2

Step-by-step explanation:

Two curves are y²=x .....(1),

and y=x² .......(2)

Now, the slope of the tangent at point(0,0) to the curves (1) and (2) are to be determined.

First, consider the curve (1).

Differentiating with respect to x, we get, 2y(dy/dx)=1, ⇒dy/dx=1/2y

Hence, the slope of tangent at (0,0) is = 1/0 =∞

Therefore, the tangent is nothing but the y-axis.

Now, consider the curve (2).

Differentiating with respect to x, we get, (dy/dx)=2x, ⇒dy/dx=2x

Hence, the slope of tangent at (0,0) is = 0

Therefore, the tangent is nothing but the x-axis.

Hence, the angle of intersection between curves (1) and (2) is 90° or π/2. (Answer)