Question

when circle p is plotted on a coordinate plane, the equation of the diameter that passes through point q on the circle is $y = 4x + 2$. which describes the equation of a line that is tangent to circle p at point q? a. the slope of the tangent line is $\frac{1}{4}$. b. the slope of the tangent line is 4. c. the slope of the tangent line is $-\frac{1}{4}$. d. the slope of the tangent line is -4.

Explanation:

Step1: Identify diameter slope

The diameter line is $y=4x+2$, so slope $m_1=4$.

Step2: Use perpendicular slope rule

Tangent is perpendicular to diameter. For perpendicular lines, $m_2 = -\frac{1}{m_1}$.
$m_2 = -\frac{1}{4}$

Answer:

C. The slope of the tangent line is $-\frac{1}{4}$.