Question

answer attempt 1 out of 2 \\(\tan(\theta) = \square\\) because tangent is the ratio of point bs \\(\dots\\) to \\(\dots\\) horizontal displacement from the y - axis vertical displacement from the x - axis distance from the origin

Explanation:

Step1: Recall tangent definition

For a point $(x,y)$ on a circle, $\tan(\theta) = \frac{y}{x}$

Step2: Identify point coordinates

Point $M$ has coordinates $(2p, -q)$, so $x=2p$, $y=-q$

Step3: Substitute into tangent formula

$\tan(\theta) = \frac{-q}{2p}$
This ratio is vertical displacement from the x-axis to horizontal displacement from the y-axis.

Answer:

$\tan(\theta) = \boldsymbol{\frac{-q}{2p}}$ because tangent is the ratio of Point B's vertical displacement from the x-axis to its horizontal displacement from the y-axis