[If the co-ordinates ofa variable point P be (cos θ + sin θ, sin θ-

1.	[If the co-ordinates ofa variable point P be (cos θ + sin θ, sin θ-cos0), where θ is a variable quantity, find the locus of P.]
Answer» P = (x1, y1) = (cosx+sinx, sinx-cosx) x1 = cosx+sinxy1 = sinx-cosx , quadr the eq's => (x1)² = (cosx+sinx)² = cos²x + sin²x + 2sinxcosx(y1)² = (sinx-cosx)² = sin²x + cos²x - 2sinxcosx , add the eq's (x1)² + (y1)² = 2It's a circle with center (0, 0) and radius √2

[If the co-ordinates ofa variable point P be (cos θ + sin θ, sin θ-cos0), where θ is a variable quantity, find the locus of P.]

Answer»

P = (x1, y1) = (cosx+sinx, sinx-cosx)

x1 = cosx+sinxy1 = sinx-cosx , quadr the eq's =>

(x1)² = (cosx+sinx)² = cos²x + sin²x + 2sinxcosx(y1)² = (sinx-cosx)² = sin²x + cos²x - 2sinxcosx , add the eq's

(x1)² + (y1)² = 2It's a circle with center (0, 0) and radius √2