If `ax+x^(2)=y^(2)-ay`, what is a in terms of x and y?

Equation of the circle on the common chord of the circles x ^(2) + y ^(2) -ax =0 and x ^(2) + y ^(2) - ay =0 as a diameter is

If the area bounded by the parabola y= ax^(2) and x= ay^(2) , a gt 0 is 1 square unit , then the value of a is-

The circle x^(2)+y^(2)-2ax-2ay+a^(2)=0 touches axes of co ordinates at

The circle x^(2)+y^(2)-2ax-2ay+a^(2)=0 touches axes of co ordinates at

If ax+by=6, bx-ay=2and x^(2)+y^(2)=4 then what is (a^(2)+b^(2)) ?

Two circles x^(2) + y^(2) + ax + ay - 7 = 0 and x^(2) + y^(2) - 10x + 2ay + 1 = 0 will cut orthogonally if the value of a is

Two circles x^(2) + y^(2) + ax + ay - 7 = 0 and x^(2) + y^(2) - 10x + 2ay + 1 = 0 will cut orthogonally if the value of a is

If ax+by=6,bx-ay=2 and x^(2)+y^(2)=4, then the value of (a^(2)+b^(2)) would be: