Question

instructions solve the following problem and choose the best answer. question in the figure above, which of the lettered points could be a point of intersection of the circle $x^{2}+y^{2}=25$ and the line $y = 3? a b c d

Explanation:

Step1: Substitute y = 3 into circle equation

Substitute \(y = 3\) into \(x^{2}+y^{2}=25\), we get \(x^{2}+3^{2}=25\).

Step2: Solve for x

\(x^{2}+9 = 25\), then \(x^{2}=25 - 9=16\), so \(x=\pm4\). The intersection points are \((4,3)\) and \((- 4,3)\). Looking at the circle \(x^{2}+y^{2}=25\) (center at origin, radius \(r = 5\)), the point with \(y = 3\) in the figure is point \(A\).

Answer:

A. A