Question

For all value of the co-ordinates of a moving point Pare (a cos θ, b sin θ); what will be the equation to the locus of P?

(a) x^2/a^2 +  y^2/b^2 = 0

(b) x^2/b^2 +  y^2/a^2 = 0

(c) x^2/b^2 +  y^2/a^2 = 1

(d) x^2/a^2 +  y^2/b^2 = 1

I had been asked this question during an online interview.

I need to ask this question from Loci of Points topic in chapter Lettering Practice, Scales & Curves of Civil Engineering Drawing

Answer 1

Right answer is (d) x^2/a^2 +  y^2/b^2 = 1

The best I can explain: Let (x, y) be the co-ordinates of any point on the locus traced out by the moving point P. Then we shall have

x = a cos θ or x/a = cos θ and y = b sin θ or, y/b = sin θ

x^2/a^2 + y^2/b^2 = cos^2 θ + sin^2 θ or, x^2/a^2 + y^2/b^2 = 1

which is the required equation to the locus of P.