If `(a^(2) + b^(2)) (x^(2) + y^(2)) = (ax + by)^(2)`, prove that : `(a)/(x) = (b)/(y)`.

If x^(a) = y^(b) = z^ (c ) and y^(2) = xz, prove that b= ( 2ac)/( a+c)

If x + i y =(a+i b)/(a-i b), prove that x^2+y^2=1 .

{:(ax - by = a^(2) + b^(2)),(x + y = 2a):}

If y^(2) = ax^(2) + b , " then " (d^(2)y)/( dx^(2))

Factorise : (iv) ax^(2) + b^(2) y - ab^(2) - x^(2) y

(prove that) If the polar of the points on the circle x^(2) + y ^(2) = a^(2) with respect to the circle x^(2) + y^(2) = b^(2) touches the circle x^(2) + y^(2) = c^(2) then prove that a, b, c, are in Geometrical progression.

If y=(a x+b)/(x^2+c), prove that (2x y_1+y)y_3=3(x y_2+y_1)y_2.

If ax^(2)+by^(2)=1 cut a'x^(2)+b'y^(2)=1 orthogonally, then

If y^2=a^2cos^2x+b^2sin^2x then prove that (d^2y)/(dx^2)+y=(a^2b^2)/(y^3)

If x+i y=(a+i b)/(a-i b) prove that x^2+y^2=1