Question

The shortest distance between the parabolas y² = x –1 and x² = y – 1 is \(\frac{3\sqrt 2}k\), then the value of k must be ____.

Answer 1

y² = x  −1...............(1)

x² = y − 1................(2)

(1) and (2) are inverse functions of each other and mirror images with respect to x = y

So, common normal both of them is always perpendicular to y = x. Slope of normal = −1

So, finding slopes of tangents on the foot of normal = 1,

The value of k is 4.