Question

Which of the following is the equation for a circle with a radius of r and center at (h, v)? A. (x + h)2 + (y + v)2 = r2 B. h2 + v2 = r2 C. (x - h)2 + (y - v)2 = r2 D. (x - v)2 + (y - h)2 = r2

Answer 1

(x - h)^2 + (y - v)^2 = r^2.

The answer would be C.

Hope this helps! :)

Answer 2

`c) (x-h)^(2)+(y-v)^(2)=r^(2)`

Explanation:

Hi There,

1. The Circle formula in its standard form is given by:

`(x-a)^(2)+(y-b)^(2)=r^(2)\Rightarrow C=(a,b)`

2) This coordinates a, b are the Center coordinates of the Center, a point distant from the circumference by the radius.

3) Because we can find derive this formula from that. (Check the graph below)

There's a point P(x,y) whose distance to C(h,v) is the radius, we need to calculate it numerically:

`r=\sqrt{(x-h)^(2)+(y-v)^(2)} \:or\:r^(2)=(x-h)^(2)+(y-v)^(2)\\r=\sqrt{x^(2)-2hx+h^(2)+y^(2)+2vy+v^(2)}\\r=\sqrt{x^(2)+h^(2)+y^(2)+v^(2)}\\(r)^(2)=(\sqrt{x^(2)+h^(2)+y^(2)+v^(2)})^(2)\\r^(2)=x^(2)+h^(2)+y^(2)+v^(2)\\r^(2)=x^(2)+y^(2)+h^(2)+v^(2)\\\\`

4) Hence, as the Center has its coordinates C(h,v) then its circle formula is:

`c) (x-h)^(2)+(y-v)^(2)=r^(2)`