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`

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

If x^(2)+y^(2)+6x-4y-12=0 then find the ragne of 2x+y

Let y = 1/6x and 4x + 12 y = 48 .What is the value of x and y?

Let P be the point on the parabola, y^2=8x which is at a minimum distance from the centre C of the circle,x^2+(y+6)^2=1. Then the equation of the circle, passing through C and having its centre at P is : (1) x^2+y^2-4x+8y+12=0 (2) x^2+y^2-x+4y-12=0 (3) x^2+y^2-x/4+2y-24=0 (4) x^2+y^2-4x+9y+18=0

If normal of circle x^(2)+y^(2)+6x+8y+9=0 intersect the parabola y^(2)=4x at P and Q then find the locus of point of intersection of tangent's at P and Q.

The number of distinct pairs (x,y) of the real number satisfying x=x^(3)+y^(4)and y=2xy is :

The number of distinct pairs (x,y) of the real number satisfying x=x^(3)+y^(4) and y=2xy is

If (x+y) = 12 and (x-y) = 4 then (2x - 4y) = ?

4x + (6)/(y) = 15 and 6x -(8)/(y) = 14 , and hence, find p if y = px - 2.