SOLUTION: Write the equations in standard form. 1) x^2 - 2x + y^2 +4y = 11 2)4x^2 + 24x - y + 34 = 0

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Write the equations in standard form. 1) x^2 - 2x + y^2 +4y = 11 2)4x^2 + 24x - y + 34 = 0      Log On


   

Question 324367: Write the equations in standard form.
1) x^2 - 2x + y^2 +4y = 11
2)4x^2 + 24x - y + 34 = 0
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1) Complete the square in x and y.
+x%5E2+-+2x+%2B+y%5E2+%2B4y+=+11
%28x%5E2-2x%2B1%29%2B%28y%5E2%2B4y%2B4%29=11%2B1%2B4
%28x-1%29%5E2%2B%28y%2B2%29%5E2=16
A circle centered at (1,-2) with a radius of 4.
.
.
.
2) Complete the square in x.
4x%5E2+%2B+24x+-+y+%2B+34+=+0
y=4x%5E2%2B24x%2B34
y=4%28x%5E2%2B6x%29%2B34
y=4%28x%5E2%2B6x%2B9%29%2B34-36
y=4%28x%2B3%29%5E2-2
A parabola with a vertex at (-3,-2).