What is the equation of a circle with its center at (0,3) and a diameter of 6.
Answers:
a. x^2+(y+3)^2=9
b. x^2-(y-3)^2=9
c. x^2+y^2-6y=0
d. x^2+(y_3)^2=0
e. x^2+(y-3)^2=36
If we know that the equation of a circle with the centre at (x0,y0) and radius r:
(x-x0)² + (y-y0)² = r²
Which choice would you take?
I think it's b.
b. is correct!
To find the equation of a circle, we need to know the coordinates of its center and the radius. In this case, the center is given as (0, 3) and the diameter is given as 6.
The radius of the circle is half of the diameter. So, the radius is 6/2 = 3.
The equation of a circle with center (h, k) and radius r is given by:
(x - h)^2 + (y - k)^2 = r^2
Plugging in the values from our given circle, the equation becomes:
(x - 0)^2 + (y - 3)^2 = 3^2
Simplifying further, we have:
x^2 + (y - 3)^2 = 9
So, the correct answer is option a. x^2 + (y + 3)^2 = 9.