Question -
Answer -
The equations of the givencurves are given as
Putting x = y2 in xy = k,we get:
Thus, the point ofintersection of the given curves is
Differentiating x = y2 withrespect to x, we have:
Therefore, the slope of thetangent to the curve x = y2 atis 
On differentiating xy = k withrespect to x, we have:
∴ Slope of the tangent to the curve xy = k atis given by,
We know that two curvesintersect at right angles if the tangents to the curves at the point ofintersection i.e., at
are perpendicular to each other.
This implies that we should have the product of thetangents as − 1.
Thus, the given two curves cut at right angles if theproduct of the slopes of their respective tangents at is −1.
Hence, the given two curves cut at rightangels if 8k2 = 1.