Question

What is the equation of the circle in general form?

Responses

x2+y2+2x+8y−47=0
x squared plus y squared plus 2 x plus 8 y minus 47 equals 0

x2+y2−2x−8y−47=0
x squared plus y squared minus 2 x minus 8 y minus 47 equals 0

x² + y² + 2x + 8y + 9 = 0
x, ² +, y, ² + 2, x, + 8, y, + 9 = 0

x2+y2−2x−8y+9=0
x squared plus y squared minus 2 x minus 8 y plus 9 equals 0

A circle on a coordinate plane centered at begin ordered pair 1 comma 4 end ordered pair. The horizontal x-axis ranges from negative 10 to 10 in increments of 1. The vertical y-axis ranges from negative 6 to 14 in increments of 1. The circle passes through begin ordered pair negative 7 comma 4 end ordered pair, begin ordered pair 1 comma 12 end ordered pair, begin ordered pair 9 comma 4 end ordered pair, and begin ordered pair 1 comma negative 4 end ordered pair.

Answer 1

To find the equation of the circle in general form, we can use the standard form equation of a circle:

(x - h)^2 + (y - k)^2 = r^2

where (h,k) is the center of the circle and r is the radius.

We are given that the center of the circle is (1,4). To find the radius, we can use the distance formula between the center and any point on the circle, such as (-7,4):

r = sqrt[(x2 - x1)^2 + (y2 - y1)^2]
r = sqrt[(-7 - 1)^2 + (4 - 4)^2]
r = sqrt[64]
r = 8

So the equation of the circle in standard form is:

(x - 1)^2 + (y - 4)^2 = 64

To convert this to general form, we can expand the squared terms and simplify:

(x^2 - 2x + 1) + (y^2 - 8y + 16) = 64
x^2 - 2x + y^2 - 8y - 47 = 0

Therefore, the equation of the circle in general form is x^2 - 2x + y^2 - 8y - 47 = 0.