Question

The center of a circle is 5 units below the origin, and the radius is 10 units. what is the equation of the circle?

Answer 1

Answer:(c)

Step-by-step explanation:

Given

the radius of circle=10 units

The center is 5 units below the origin i.e. (0,-5) is the center

The general equation of a circle is

$(x-a)^2+(y-b)^2=r^2\quad [\text{Where, (a,b) is the center of the circle and r is radius}]$

Putting values

$(x-0)^2+(y-(-5))^2=10^2\\(x)^2+(y+5)^2=100$

Second last option is correct

Answer 2

Answer:

x² + (y + 5)² = 100

Step-by-step explanation:

If the center of the circle is 5 units below the origin, its x coordinate is 0 and its y-coordinate is -5. So, the center of the circle is at (0, -5).

Using the equation of a circle with center (h, k)

(x - h)² + (y - k)² = r² where r = radius of the circle.

Given that r = 10 units, and substituting the values of the other variables into the equation, we have

(x - h)² + (y - k)² = r²

(x - 0)² + (y - (-5))² = 10²

x² + (y + 5)² = 100

which is the equation of the circle.