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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 |
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Answer» 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. |
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