Question

If tangent OX and OY of curve √x – √y = √a at some point cut the axis at point P and Q, then show that OP + OQ – a, where O is origin.

Answer 1

Given,

Equation √x – √y = √a …..(i)

Let, tangent cut the axis OX and OY at point P and Q, point on curve contact with tangent is (h, k).

Since, (h, k) situated on curve.

So, √x – √y = √a …..(ii)

Diff. (i) w.r.t. x,

So, from y – y₁ = m(x – x₁) equation of tangent at the point (h, k).