The distance between the origin and the point nearest to it on the surface z^{2} = 1 + xy is

- a)1
- b)√3/2
- c)√3
- d)-2

Correct answer is option 'A'. Can you explain this answer?

By
Vivek Jangir
·
3 weeks ago ·Mechanical Engineering

Divya Gaur
answered
Jul 16, 2018

or pr – q^2 = 4 – 1 = 3 > 0 and r = +ve

so f(xy) is minimum at (0,0)

Hence, minimum value of d^2 at (0,0)

d2 = x^2 + y^2 + xy + 1 = (0)^2 + (0)^2 + (0)(0) + 1 = 1

Then the nearest point is

z^2 = 1 + xy = 1+ (0)(0) = 1

or z = 1

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