Question

multiple choice 10 points which is the equation of a circle whose center is at the origin and that passes through the point (3, 5)? $x^2 + y^2 = 16$ $x^2 + y^2 = 34$ $(x - 3)^2 + (y - 5)^2 = 34$ $(x - 3)^2 + (y - 5)^2 = 16$ clear my selection previous

Explanation:

Step1: Recall the circle equation

The standard equation of a circle with center \((h,k)\) and radius \(r\) is \((x - h)^2+(y - k)^2=r^2\). Since the center is at the origin \((0,0)\), the equation becomes \(x^2 + y^2=r^2\).

Step2: Find the radius squared

The circle passes through the point \((3,5)\). Substitute \(x = 3\) and \(y = 5\) into the equation \(x^2 + y^2=r^2\). So \(r^2=3^2 + 5^2=9 + 25 = 34\).

Step3: Write the circle equation

Substituting \(h = 0\), \(k = 0\) and \(r^2=34\) into the standard circle equation, we get \(x^2 + y^2=34\).

Answer:

\(x^2 + y^2 = 34\) (the option with this equation)