SOLUTION: I need to know how to state whether certain graphs of an equation are a parabola, an ellipse, or a hyperbola. Some equations I'm given to determine these are: (number)=exponent

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: I need to know how to state whether certain graphs of an equation are a parabola, an ellipse, or a hyperbola. Some equations I'm given to determine these are: (number)=exponent       Log On


   

Question 724506: I need to know how to state whether certain graphs of an equation are a parabola, an ellipse, or a hyperbola. Some equations I'm given to determine these are:
(number)=exponent
1. y(2)+5=4(x+y)
2. 2x(2)=8x-y(2)
3. 4(y+1)(y-1)+5x(2)=24
Please and thanks for your help!
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
1. y(2)+5=4(x+y)
y^2+5=4x+4y
y^2-4y=4x-5
complete the square:
(y^2-4y+4)=4x-5+4
(y-2)^2=4x-1
%28y-2%29%5E2=4%28x-1%2F4%29
This is an equation of a parabola that opens rightward
Its basic form: %28y-k%29%5E2=4p%28x-h%29, (h,k)=(x,y) coordinates of the vertex
..
2. 2x(2)=8x-y(2)
2x^2+8x+y^2=0
complete the square
2(x^2+4x+4)+y^2=0+8
2(x+2)^2+y^2=8
%28x%2B2%29%5E2%2F4%2By%5E2%2F8=1
This is an equation of an ellipse with vertical major axis
Its standard form: %28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2, a>b, (h,k)=(x,y) coordinates of the center
..
3. 4(y+1)(y-1)+5x(2)=24
4(y^2-1)+5x^2=24
4y^2-4+5x^2=24
4y^2+5x^2=24+4
4y^2+5x^2=28
y%5E2%2F7%2Bx%5E2%2F%2828%2F5%29=1
This is an equation of an ellipse with horizontal major axis
Its standard form: %28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2, a>b, (h,k)=(x,y) coordinates of the center