Question

(x - 7)^2 + (y + 5)^2 = 16
the given equation represents a circle in the xy - plane. if (x, - 5) is a point on the circle, what is a possible value of x?

Explanation:

Step1: Substitute \( y = - 5 \) into the equation

Substitute \( y=-5 \) into \((x - 7)^{2}+(y + 5)^{2}=16\).
We get \((x - 7)^{2}+(-5 + 5)^{2}=16\), which simplifies to \((x - 7)^{2}+0^{2}=16\), so \((x - 7)^{2}=16\).

Step2: Solve for \( x \)

Take the square root of both sides: \(x - 7=\pm\sqrt{16}\).
Since \(\sqrt{16} = 4\), we have two cases:
Case 1: \(x - 7=4\), then \(x=4 + 7=11\).
Case 2: \(x - 7=-4\), then \(x=-4 + 7=3\).

Answer:

\(3\) or \(11\)