write the standard form of the equation of the circle withthe given radius (8,0) and whose center is the origin
The given radius of (8,0) does not look right, since radius is a scalar, it should not have two components.
The standard form of the circle, centred at (x0,y0) with radius r is given by:
C : (x-x0)²+(y-y0)² = r²
To write the standard form of the equation of the circle with the given radius (8, 0) and whose center is the origin, we can use the formula for the equation of a circle.
The equation of a circle with center (h, k) and radius r is given by:
(x - h)^2 + (y - k)^2 = r^2
In this case, the center of the circle is the origin (0, 0), so we can substitute h = 0 and k = 0 into the equation.
(x - 0)^2 + (y - 0)^2 = r^2
x^2 + y^2 = r^2
Since the radius of the given circle is (8, 0), we substitute r = 8 into the equation.
x^2 + y^2 = 8^2
x^2 + y^2 = 64
Therefore, the standard form of the equation of the circle with a radius of (8, 0) and center at the origin is x^2 + y^2 = 64.