Question

point q lies on the circle and has an x-coordinate of 4. which value could be the y-coordinate for point q? 2√13, 2√5, 4√2, 8√2

Explanation:

Step1: Determine the circle's equation

The circle is centered at \((0,0)\) and passes through \((6,0)\), so the radius \(r = 6\). The equation of the circle is \(x^{2}+y^{2}=r^{2}=36\).

Step2: Substitute \(x = 4\) into the equation

Substitute \(x = 4\) into \(x^{2}+y^{2}=36\):
\(4^{2}+y^{2}=36\)
\(16 + y^{2}=36\)

Step3: Solve for \(y\)

Subtract 16 from both sides:
\(y^{2}=36 - 16=20\)
Take the square root:
\(y=\pm\sqrt{20}=\pm2\sqrt{5}\)

Answer:

\(2\sqrt{5}\)