" 8."(x^(-2/3)y^(-1/2))^(2)

If (x^(2) + y^(2))/(x^(2) - y^(2)) = 2(1)/(8) , find : (i) (x)/(y) (ii) (x^(3) + y^(3))/(x^(3) - y^(3))

If the circles (x-1)^(2)+(y-3)^(2)=4r^(2) and x^(2)+y^(2)-8x+2y+8=0 intersect in two distinct points, then show that 1ltrlt 4 .

The following are the steps involved in factorizing 64 x^(6) -y^(6) . Arrange them in sequential order (A) {(2x)^(3) + y^(3)} {(2x)^(3) - y^(3)} (B) (8x^(3))^(2) - (y^(3))^(2) (C) (8x^(3) + y^(3)) (8x^(3) -y^(3)) (D) (2x + y) (4x^(2) -2xy + y^(2)) (2x - y) (4x^(2) + 2xy + y^(2))

The locus of a point "P" ,if the join of the points (2,3) and (-1,5) subtends right angle at "P" is x^(2)+y^(2)-x-8y+13=0 x^(2)-y^(2)-x+8y+3=0 x^(2)+y^(2)-4x-4y=0,(x,y)!=(0,4)&(4,0) x^(2)+y^(2)-x-8y+13=0,(x,y)!=(2,3)&(-1,5)

Find the 8 th term in the expansion of (x^((3)/(2))y^((1)/(2))-x^((1)/(2))y^((3)/(2)))^(10)

If (x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3)) are vertices of equilateral triangle such that (x_(1)-2)^(2)+(y_(1)-3)^(2)=(x_(2)-2)^(2)+(y_(2)-3)^(2)=(x_(3)-2)^(2)+(y_(3)-3)^(2) then

(x+1)/(2)+(y-1)/(3)=8;(x-1)/(3)+(y+1)/(2)=9