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`

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

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

Find the distance between the pair of parallel lines x^2+4x y+4y^2+3x+6y-4=0

Find the distance between the pair of parallel lines x^2+4x y+4y^2+3x+6y-4=0

Find the distance between the pair of parallel lines x^2+4x y+4y^2+3x+6y-4=0

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

Find the centre and radius of the circle x^(2) + y^(2) - 6x + 4y - 12 =0 .

Find the number of ordered pair of real numbers (x, y) satisfying the equation: 5x(1+1/(x^(2)+y^(2)))=12 & 5y(1-1/(x^(2) + y^(2))) =4

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

If 3x+2y=12 and x y=6 , find the value of 9x^2+4y^2