A circle has the equation
x^2+y^2+6x-46=0
graph using (h,k) radius r
A) how do i graph this properly
B) intercept are?
To graph the given equation of a circle, x^2 + y^2 + 6x - 46 = 0, we need to first rewrite it in center-radius form, which is (x - h)^2 + (y - k)^2 = r^2.
Step A) How to graph the equation properly:
1. Complete the square: Move the constant term (-46) to the other side of the equation to isolate the x and y terms.
x^2 + y^2 + 6x = 46
2. To complete the square for the x-terms, take half of the x-coefficient (6) and square it, then add it to both sides of the equation.
x^2 + 6x + (6/2)^2 = 46 + (6/2)^2
x^2 + 6x + 9 = 46 + 9
x^2 + 6x + 9 = 55
3. Repeat the same process for the y-terms.
y^2 = -x^2 - 6x + 55
4. Now, rearrange the equation into the standard form by factoring the x-terms and y-terms.
x^2 + 6x + 9 + y^2 = 55
(x + 3)^2 + y^2 = 55
5. From the equation, we can now identify the center (h, k) and radius (r) of the circle.
Center (h, k) = (-3, 0)
Radius (r) = sqrt(55)
Now that we have identified the center and radius, we can proceed to graph the equation.
To graph the circle:
1. Plot the center point (-3, 0) on a graph.
2. From the center, measure the distance of the radius (sqrt(55)) in each direction.
In this case, since the radius is positive, measure sqrt(55) units up, down, left, and right from the center.
3. Draw a smooth curve connecting the points to form the circle.
Step B) Finding the intercepts:
To find the intercepts, we set x and y to zero and solve for the other variable.
1. To find the x-intercepts, set y = 0:
x^2 + 6x + 9 + 0 = 55
x^2 + 6x + 9 = 55
x^2 + 6x - 46 = 0
Now, solve the quadratic equation to find the x-intercepts. You can use factoring, completing the square, or the quadratic formula to solve for x.
2. To find the y-intercepts, set x = 0:
0^2 + y^2 + 6(0) - 46 = 0
y^2 - 46 = 0
Again, solve this quadratic equation to find the y-intercepts.
By solving these equations, you will obtain the x and y coordinates of the intercepts of the circle.