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?

x^2+(y+5)=10

(x+5)^2+y^2=10

x^2 + (y+5)^2=100

(x+5)^2+y^2=100

Answer 1

Answer:(c)

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

x² + (y + 5)² = 100

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.