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Need help please asap

Need help please asap-example-1
User AndyG
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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

User Schot
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