The number of point (s)`(x,y)` (where x and y both are perfect squares of integers) on the parabola `y ^(2)=px` ,p being a prime number,is

The number of solutions (x, y) where x and y are integers, satisfying 2x^(2) + 3y^(2) + 2x + 3y=10 is:

Find the point where the line x+y=6 is a normal to the parabola y^2=8x .

The number of points (x,y) satisfying y=2 sinx and y=x^2+2 is

The number of pairs of positive integers (x,y) where x and y are prime numbers and x^(2)-2y^(2)=1 , is

The number of integral points (x,y) (i.e, x and y both are integers) which lie in the first quadrant but not on the coordinate axes and also on the straight line 3x + 5y = 2007 is equal to

Is x^2 - 6xy + 36y^2 a perfect square trinomial ?

The number of points on the curve y=x^(3)-2x^(2)+x-2 where tangents are prarllel to x-axis, is

The number of chords drawn from point (a, a) on the circle x^(2)+y"^(2)=2a^(2) , which are bisected by the parabola y^(2)=4ax , is

Prove that the focal distance of the point (x ,y) on the parabola x^2-8x+16 y=0 is |y+5|

Prove that the focal distance of the point (x ,y) on the parabola x^2-8x+16 y=0 is |y+5|