SOLUTION: WW 1.3 Determine whether the equation is a circle or parabola and transform the general equation to standard equation. If the equation is a circle, you need to identify the c

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: WW 1.3 Determine whether the equation is a circle or parabola and transform the general equation to standard equation. If the equation is a circle, you need to identify the c      Log On


   

Question 1197082: WW 1.3
Determine whether the equation is a circle or parabola and transform the general equation to standard equation.
If the equation is a circle, you need to identify the center and radius of the circle with the given equation in each item. Sketch
its graph and label the 2 parts of the circle.
If the equation is a parabola, you need to identify the opening, vertex, focus, latus rectums, axis of symmetry and directrix of the parabola. Sketch its graph and label the 6 parts of the parabola.
1. x²+ y²-6x= 7
2. x²+8y8x+40= 0
3.9x2+9y²+54x - 36y + 36 = 0
4. x²-8x - y +9 = 0
Found 2 solutions by math_tutor2020, josgarithmetic:
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

I'll do problem 1 to get you started.
In the future please only post one problem at a time.

x^2 = x%5E2

x^2+y^2-6x = 7
(x^2-6x)+y^2 = 7
(x^2-6x+9)+y^2 = 7+9
(x-3)^2+y^2 = 16

This graphs out a circle centered at (3,0) with radius r = 4

Use this template
(x-h)^2 + (y-k)^2 = r^2
center = (h,k)
radius = r

Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
#3:

9x2+9y²+54x - 36y + 36 = 0

9x%5E2%2B9y%5E2%2B54x-36y%2B36=0
x%5E2%2By%5E2%2B6x-4y%2B4=0
x%5E2%2B6x%2By%5E2-4y%2B4=0
9 completes the square for x.
4 completes the square for y. (already present in the equation)
%28x%5E2%2B6x%2B9%29%2B%28y%5E2-4y%2B4%29=0%2B9
%28x%2B3%29%5E2%2B%28y-2%29%5E2=9
%28x%2B3%29%5E2%2B%28y-2%29%5E2=3%5E2-----------the rest of the meaning and what to do should be already clear from here.