Solve Math Algebra II?

Question

I have to solve conic math problems and I'm having major trouble! Can someone help me understand these kinds of problems;

Find the center and radius.

1. 2x^2 + 2y^2 - 2x - 10y + 10 > 0

Classify the conic section.

2. 36x^2 + 16y^2 - 25x + 22y + 2 > 0

3. 16y^2 - x^2 + 2x + 62y + 63 = 0

Answer 1

1. 2x^2 + 2y^2 - 2x - 10y + 10 > 0


2x^2 + 2y^2 - 2x - 10y + 10 > 0. Divide by 2,

x^2 + y^2 - x - 5y + 10 > 0

Group the x-terms and y-terms together.

x^2 - x + y^2 - 5y + 10 > 0

Move the 10 to the right hand side.

x^2 - x + y^2 - 5y > -10

Complete the square for the x and y terms.

[x^2 - x + (1/4)] + [y^2 - 5y + (25/4)] > -10 + (1/4) + (25/4)

[x - (1/2)]^2 + [y - (5/2)]^2 > -40/4 + 1/4 + 25/4

[x - (1/2)]^2 + [y - (5/2)]^2 > -14/4

Two squared terms are positive, and will always be greater than a negative number. The answer is all real numbers x and y.

Answer 2

I think that you have wrongly typed a > sign in the first two when you meant an =.
2x^2 + 2y^2 - 2x -10y + 10 = 0 is the equation of a circle so as written with > it is everywhere outside of the circle.
Divide throughout by 2 to get x^2 + y^2 - x - 5y + 5 = 0
Rearrange this to (x - 0.5)^2 + (y - 2.5)^2 = 1.5
This shows that centre is (0.5,2.5) and radius is sqrt(1.5)
#2 is also a circle
#3 is a hyperbola