Write the equation of the circle in standard form. Find the center, radius, intercepts and graph the circle. x^2+y^2+14x+18y=-81
rearrange things a bit:
x^2+14x + y^2+18y = -81
x^2+14x+49 + y^2+18y+81 = -81 + 49 + 81
(x+7)^2 + (y+9)^2 = 49
now the rest is easy.
C'mon back if you get stuck.
my math problem is a little different, but I still got this far... my center is (8,-4) and radius is 3 square root of 10... how do I plot a radius like that?
To write the equation of a circle in standard form, we need to complete the square for both the x and y variables.
First, we rearrange the equation:
x^2 + y^2 + 14x + 18y = -81
To complete the square for the x variables, we take half the coefficient of x (which is 14/2 = 7), square it (7^2 = 49), and add it to both sides of the equation:
x^2 + 14x + 49 + y^2 + 18y = -81 + 49
Simplifying further:
(x^2 + 14x + 49) + (y^2 + 18y) = -81 + 49
To complete the square for the y variables, we take half the coefficient of y (which is 18/2 = 9), square it (9^2 = 81), and add it to both sides of the equation:
(x^2 + 14x + 49) + (y^2 + 18y + 81) = -81 + 49 + 81
Simplifying further:
(x^2 + 14x + 49) + (y^2 + 18y + 81) = 49
We can now rewrite the equation in standard form:
(x + 7)^2 + (y + 9)^2 = 49
From this equation, we can observe that the center of the circle is at (-7, -9), and the radius is the square root of 49, which is 7.
To find the x-intercepts, we set y = 0 and solve for x:
(x + 7)^2 + (0 + 9)^2 = 49
(x + 7)^2 + 81 = 49
(x + 7)^2 = 49 - 81
(x + 7)^2 = -32 (No real solution, imaginary intercepts)
To find the y-intercepts, we set x = 0 and solve for y:
(0 + 7)^2 + (y + 9)^2 = 49
49 + (y + 9)^2 = 49
(y + 9)^2 = 0
y = -9
To graph the circle, we plot the center (-7, -9) and draw a circle with a radius of 7.
I apologize, but I am unable to provide a visual representation here. However, you can plot the center (-7, -9) on a graph and draw a circle with a radius of 7 units.