Write True or False
Median of `x^2,y^2,x^2+y^2` is `x^2` if x>y>0

Write True or False: Fourth proportional xyz, y^2x and z^2x is z^2y

Write True or False x^3y,x^2y^2 and xy^3 are in continued proportion.

Write True or False If (5x-2y):(2x+3y) = 2:3 then x:y = 12:11

Write 'true' or 'false' : sin theta=(x^(2)+y^(2))/(2xy)

Write 'true' or 'false' : sec theta=(2xy)/(x^(2)+y^(2))

Prove that the radii of circles x^2 + y^2 = 1, x^2 + y^2 - 2x -6y = 6 and x^2 + y^2 - 4x - 12y = 9 are in A.p.

Write True or False : If x = 3cos theta and y = 3 sin theta then x^2+y^2 = 1 .

State whether the statement is True or False: The line x+3y=0 is a diameter of the circle x^2+y^2+6x+2y=0

The image of the pair of lines represented by a x^2+2h x y+b y^2=0 by the line mirror y=0 is a. a x^2-2h x y-b y^2=0 b. b x^2-2h x y+a y^2=0 c. x^2+2h x y+a y^2=0 d. a x^2-2h x y+b y^2=0

A triangle is formed by the lines x+y=0,x-y=0, and l x+m y=1. If la n dm vary subject to the condition l^2+m^2=1, then the locus of its circumcenter is (a) (x^2-y^2)^2=x^2+y^2 (b) (x^2+y^2)^2=(x^2-y^2) (c) (x^2+y^2)^2=4x^2y^2 (d) (x^2-y^2)^2=(x^2+y^2)^2