Explanation:
the circle standard form is
(x - h)² + (y - k)² = r²
(h, k) are the coordinates of the center of the circle.
r is the radius of the circle.
I cannot draw here, but I can describe the details.
9.
the center is therefore at (-1, 2). and the radius is 5.
to graph the circle mark the 4 points with radius distance up, down, left and right of the center.
up : (-1, 2 + 5) = (-1, 7)
down : (-1, 2 - 5) = (-1, -3)
left : (-1 - 5, 2) = (-6, 2)
right : (-1 + 5, 2) = (4, 2)
10.
the center is therefore at (3, 0). and the radius is 4.
to graph the circle mark the 4 points with radius distance up, down, left and right of the center.
up : (3, 0 + 4) = (3, 4)
down : (3, 0 - 4) = (3, -4)
left : (3 - 4, 0) = (-1, 0)
right : (3 + 4, 0) = (7, 0)
11.
we have the h, k coordinates of the center.
for the radius we need to find the distance between the center and the given point.
remember, this is via Pythagoras in a right-angled triangle
c² = a² + b²
with c being the Hypotenuse (the side opposite of the 90° angle), a and b being the legs.
for the distance between 2 points the direct distance is the Hypotenuse, and the x and y coordinate differences are the legs.
distance² = r² = (7 - 2)² + (-1 - -1)² = 5² + 0² = 5² = 25
so, the equation is
(x - 2)² + (y + 1)² = 25
12.
we have the h, k coordinates of the center.
for the radius we need to find the distance between the center and the given point.
distance² = r² = (4 - 1)² + (6 - 2)² = 3² + 4² = 9 + 16 = 25
so, the equation is
(x - 1)² + (y - 2)² = 25