A B is a line segment moving between the axes such that ' A ' lies on X -axis and ' B ' lies on Y -axis. If P is a point on A B such that P A=b and P B=a , then the equation of locus of P is

Step-by-step solution

Let P(h, k) be any point in the locus cm Let A=(x, 0), B=(0, y) Given, P A=b, P B=a In P M A , = k b In B N P , = h a We have, aligned ^2 + ^2 & =1 k^2 b^2 + h^2 a^2 & =1 h^2 a^2 + k^2 b^2 & =1 aligned Required locus of point P(h, k) is x^2 a^2 + y^2 b^2 =1 Hence, option (2) is correct.