Examing whether point `(2, -3)` lies on the curve `x^2 - 2y^2 + 6xy + 8 =0`.

Examine whether point (1, 2) lies on the curve 4x^2 - y^2 =0 .

Examine whether point (2, -5) lies on the curve x^2 +y^2 -2x+1=0

The point (0,3) is nearest to the curve x^(2)=2y at

The point (0,3) is closest to the curve x^(2)=2y at

State whether the following are true or false (e) the point (2, 3) lies outside the circle x^2+y^2-2x+6y+1=0

State whether the point (-3,4) lies on the line, 3x+2y+1=0 or not ?

The point (1,2) lies inside the circle x^(2)+y^(2)-2x+6y+1=0 .

Find the points farthest and nearest on the curve 5x^2+5y^2+6xy -8=0 from origin.Also determine the equations of the lines through the origin on which the points are occurring.

Determine whether the point (4,-2) lies on the graph of the equation 2x+y=6 or not.