SOLUTION: Please explain how to solve this step by step: Tell which conic is identified by each equation: 1.) {{{3x^2 - 2y^2 + 3y - 9 = 0}}} 3.) {{{7x^2 + 8x - 3y + 7 = 0}}}

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Please explain how to solve this step by step: Tell which conic is identified by each equation: 1.) {{{3x^2 - 2y^2 + 3y - 9 = 0}}} 3.) {{{7x^2 + 8x - 3y + 7 = 0}}}      Log On


   

Question 807214: Please explain how to solve this step by step:
Tell which conic is identified by each equation:
1.) 3x%5E2+-+2y%5E2+%2B+3y+-+9+=+0
3.) 7x%5E2+%2B+8x+-+3y+%2B+7+=+0
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Tell which conic is identified by each equation:
1.) 3x%5E2+-+2y%5E2+%2B+3y+-+9+=+0
3.) 7x%5E2+%2B+8x+-+3y+%2B+7+=+0
***
1.) 3x%5E2+-+2y%5E2+%2B+3y+-+9+=+0
3x^2 - 2y^2 + 3y - 9 = 0
3x^2 - 2y^2 + 3y =9
complete the square:
3x^2-2(y^2-3y/2+9/16)=-9/8+9
3x^2-2(y-3/4)^2=63/8
This is an equation of a hyperbola with horizontal transverse axis.
Its standard form: %28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1, (h,k)=(x,y) coordinates of center
..
3.) 7x%5E2+%2B+8x+-+3y+%2B+7+=+0
7x^2 + 8x - 3y + 7 = 0
7x^2 + 8x +7 = 3y
complete the square:
7(x^2+8x/7+64/196)+7= 3y+64/28
7(x+8/14)^2+7-64/28=3y
This is an equation of a parabola that opens upwards:
Its standard form: y=A%28x-h%29%5E2%2Bk, (h,k)=(x,y) coordinates of the vertex