Equation of a circle
(x-h)^2+(y-k)^2=r^2
The equation of a circle is given by:
(x − h)² + (y − k)² = r²
Where (h, k) represents the center of the circle, and r represents its radius.
This equation can also be written in the standard form as:
x² + y² + 2gx + 2fy + c = 0
Where g = h, f = k and c = h² + k² − r².
This form is used to find the equation of a circle when the center and radius are not given explicitly. To obtain this form, we complete the square of the equation (x − h)² + (y − k)² = r² by expanding the squares and then grouping the x and y terms separately from constants to obtain the standard form.
To graph a circle with the equation, we can find its center and radius, plot the center point on the coordinate plane, and then draw a circle with the given radius around the center. We can also use the Pythagorean theorem to find points on the circle given one coordinate and the equation.
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