" If "x^(2)+y^(2)=1," show that,"(3x-4x^(3))^(2)+(3y-4y^(3))^(2)=1

If x^(2)+y^(2)=1 and P=(3x-4x^(3))^(2)+(3y-4y^(3))^(2) then P is equal to

If x^2+y^2=1 and P=(3x-4x^3)^2+(3y-4y^3)^2 then P is equal to

IF x^2+y^2=1 and P=(3x-4x^3)^2+(3y-4y^3)^2 then find 'P'.

If y=x+x^(2)/2+x^(3)/3+x^(4)/4+... then show that x=y-y^(2)/(2!)+y^(3)/(3!)-y^(4)/(4!)+...

Identify the type of conic section for each of the equations 1. 2x^(2) -y^(2) = 7 2. 3x^(2) +3 y^(2) -4x + 3y + 10 =0 3. 3x^(2) + 2y^(2) = 14 4. x^(2) + y^(2) + x-y=0 5. 11x^(2) -25y^(2) -44x + 50y - 256 =0 6. y^(2) + 4x + 3y + 4=0

{:("Column" A ,, "Column" B), ((3x^(2) - 5)- (2x^(2) - 5 + y^(2)) ,, (a) x^(2) + xy + y^(2)) , (9x^(2) - 16y^(2) ,, (b) 2) , ((x^(3) - y^(3))/(x-y) ,, (c) (9x + 16y) (9x - 16y)) , ("The degree of " (x + 2) (x+3) ,, (d) x^(2) - y^(2)) , (,, (e) 1) , (,, (f) (3x + 4y) (3x - 4y)):}

2x-3y-3=0; (2x)/(3)+4y+(1)/(2)=0