LexiRea85
contestada

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 statement describes the equation of a line that is tangent to circle P at point Q? A. The slope of the tangent line is 4. B. The slope of the tangent line is . C. The slope of the tangent line is -4. D. The slope of the tangent line is .

Respuesta :

MrRoyal

The true statement about the equation of the tangent line is (a) the slope of the tangent line y = 4x + 2 is 4

How to interpret the tangent line?

The equation of the tangent line is given as:

y = 4x + 2

A linear equation is represented as:

y = mx + b

Where:

m represents the slope

By comparison;

m = 4

This means that the slope of the tangent line is 4

Hence, the true statement is (a)

Read more about tangent lines at:

https://brainly.com/question/6617153

#SPJ1

semsee45

Answer:

[tex]\sf D.\quad \textsf{The slope of the tangent line is }-\dfrac{1}{4}[/tex]

Step-by-step explanation:

Slope-intercept form of a linear equation:  [tex]\sf y=mx+b[/tex]

(where m is the slope and b is the y-intercept).

The equation of the diameter is [tex]\sf y=4x+2[/tex], therefore its slope is 4.

The tangent of a circle is always perpendicular to the radius, which means it is also perpendicular to the diameter.

If two lines are perpendicular to each other, the product of their slopes is -1.

[tex]\begin{aligned}\textsf{slope of diameter} \times \textsf{slope of tangent} & =-1\\\implies 4 \times \textsf{slope of tangent} & =-1\\\implies \textsf{slope of tangent} & = -\dfrac{1}{4}\end{aligned}[/tex]

Therefore, the slope of the tangent line is [tex]\sf -\dfrac{1}{4}[/tex]

Ver imagen semsee45

Otras preguntas