Find Whether the point (2,6) lies on, inside or outside the parabola 2x - y2 + 2y +3 = 0.

Dear pratik

2x - y² + 2y +3 = 0

convert it in to standard form

(y-1)² -2(x+2)=0

let S =(y-1)² -2(x+2)

now put point S1 =17>0

 so point lie outside the parabola

now solve it with another method

 let S =2x - y² + 2y +3

put point

S1= -17

 this result gives that point lie inside the parabola

but you should careful that in standard form coefficient of y²   

 is positive so you must take  y² as a positive coefficient in general form

so you will take S =-2x + y² - 2y -3

Regards

Badiuddin