Question

The distance between the origin and the point (2, -3)

Answer 1

Answer:

Let point on curve be P(acosecθ,bsecθ)

distance from origin OP=a2cosec2θ+b2sec2θ

=a2+a2cot2θ+b2+b2tan2θ

=a2+b2+(acotθ−btanθ)2+2ab

=(a+b)2+(acotθ−btanθ)2

So, under the square root we have sum of two square terms, the first of which is a constant and second is a function of θ. The minimum value of second term is 0.

So, OPmin.=a+b