Question

What is the general form of the equation for the given circle centered at O(0, 0)?

Answer 1

The correct answer is option B

Explanation:

B. x2 + y2 − 41 = 0

Answer 2

let's notice that the center of the circle is at the orgin, and that the distance from the center to an endpoint B is its radius.

`\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ O(\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad B(\stackrel{x_2}{4}~,~\stackrel{y_2}{5})\qquad \qquad d = √(( x_2- x_1)^2 + ( y_2- y_1)^2)`

`\bf \stackrel{radius}{r}=√((4-0)^2+(5-0)^2)\implies r=√(4^2+5^2) \\\\\\ r=√(16+25)\implies r=√(41) \\\\[-0.35em] ~\dotfill\\\\ \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{0}{ h},\stackrel{0}{ k})\qquad \qquad radius=\stackrel{√(41)}{ r} \\\\\\ (x-0)^2+(y-0)^2=(√(41))^2\implies x^2+y^2=41`