SOLUTION: Find: a) (h,k) and radius r b) Graph the circle c) Find intercepts, if any (x^2)+(y^2)+x+y-(1/2)=0 or (x^2)+x+(y^2)+y=(1/2)

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Question 1026883: Find:
a) (h,k) and radius r
b) Graph the circle
c) Find intercepts, if any
(x^2)+(y^2)+x+y-(1/2)=0 or (x^2)+x+(y^2)+y=(1/2)
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Find:
a) (h,k) and radius r
b) Graph the circle

(x^2)+(y^2)+x+y-(1/2)=0 or (x^2)+x+(y^2)+y=(1/2)
===========
x^2+x+y^2+y=1/2
Complete the squares for x and y
x^2+x+1/4 + y^2+y+1/4 = 1/2+1/4+1/4 = 1
(x+1/2)^2 + (y+1/2)^2 = 1
(h,k) = (-1/2,-1/2)
r = 1
-------------
c) Find intercepts, if any
x^2+x+y^2+y=1/2
y = 0 --> x^2 + x - 1/2 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=3 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 0.366025403784439, -1.36602540378444. Here's your graph:

================
Intercepts are (x1,0) and (x2,0)
By symmetry, the y-ints are (0,x1) and (0,x2)


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