`y^(2)=4x, y^(2)=4(4-x)`

Find the area of the region {(x,y):y^(2)<=4x,4x^(2)+4y^(2)<=9}

Find the area of the region {(x,y):y^(2)<=4x,4x^(2)+4y^(2)<=9}

Find the area of the region ,{(x,y):y^(2)<=4x,4x^(2)+4y^(2)<=9}

Simplify each of the following: (4x+2y)^(2)+(4x-2y)^(2)(4x+2y)^(3)-(4x-2y)^(2)

Match the following. {:("Line, parabola"," "," ""Pole"),("I". 2x-3y+4=0,y^(2)=4x," "(a)(4,6)),("II". 2x+3y-4=0,y^(2)=4x," "(b)(2,3)),("III". x-2y+4=0,y^(2)=6x," "(c)(-2,-3)),("IV". 3x+4y-4=0,x^(2)=4y," "(d)(-3//2,-1)):}

Equation of line touching both parabolas y^(2)=4x and x^(2) = -32y is a) x+2y + 4 =0 b) 2x +y4 =0 c) x-2y-4 =0 d) x-2y+4 =0

Orthogonal trajectories of the family of curves represented by x^(2)+2y^(2)-y+c=0 is (A) y^(2)=a(4x-1)(B)y^(2)=a(4x^(2)-1)(C)x^(2)=a(4y-1)(D)x^(2)=a(4y^(2)-1)

Let y'=(4y^(2)+4xy+x^(2))/(4x^(2)) and y(1)=0 then y(e^((pi)/(2))) equals

Find the area enclosed by the curves y^2 = 4x and y^2 = 4 (4 - x) .

(3x - 4y)^(2) - (4x + 3y)^(2) = "______" .