" Q4."x=2at^(2),quad y=at^(4)

" Q."4[" The area of the smaller portion enclosed by the "],[" curves "x^(2)+y^(2)=9" and "y^(2)=8x" is "]

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

Equations of the common tangents to the parabola, y=x^(2) and y=-(x-2)^(2) are [x=0,x=4y-2],[x=0,y=4x-2],[y=0,y=4x+4],[y=0,y=4x-4]

The LCM and GCD of the two polynomilas is (x^2 + y^(2) ) (x^(4) + x^(2) y^(2) + y^(4)) and x^(2) -y^(2) one of the polynomial q(x) is (x^(4)-y^(4))(x^(2) +y^(2) - xy) find the other polynomials.

P(x)=(5)/(3)-6x-9x^(2) and Q(y)=-4y^(2)+4y+(13)/(2) if there exists unique pair of real numbers (x,y) such that P(x)Q(y)=20, then the value of (6x+10y) is

let p(x)=4x^(2)+6x+4 and q(y)=4y^(2)-12Y+25. Find the unique pairs of real numbers x and y such that P(x).Q(y)=28

The solution of the differential equation (dy)/(dx)+(x(x^(2)+3y^(2)))/(y(y^(2)+3x^(2)))=0 is (a) x^(4)+y^(4)+x^(2)y^(2)=c (b) x^(4)+y^(4)+3x^(2)y^(2)=c (c) x^(4)+y^(4)+6x^(2)y^(2)=c (d) x^(4)+y^(4)+9x^(2)y^(2)=c

If the circle x^(2)+y^(2)=a^(2) intersects the hyperbola xy=c^(2) in four points P (x_(1) ,y_(1)) Q (x_(2), y_(2)) R (x_(3) ,y_(3)) S (x_(4) ,y_(4)) then 1) x_(1)+x_(2)+x_(3)+x_(4)=2c^(2) 2) y_(1)+y_(2)+y_(3)+y_(4)=0 3) x_(1)x_(2)x_(3)x_(4)=2c^(4) 4) y_(1)y_(2)y_(3)y_(4)=2c^(4)