Question

The point P with coordinates (10, -1) lies on a circle that's centered at point C with coordinates (5, -1). Find the equation of the tangent line to the circle at P.

Answer 1

The linear equation of the tangent line to the circle at P is given by: x = -1.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

• m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

• b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

The equation of the circle, considering it's center at (5,-1) and edge at (10,-1), that is, a radius of 5, is given by:

$(x - 5)² + (y + 1)² = 25$

The slope is given by the derivative at point P, hence:

$2(x - 5) + 2(y + 1)\frac{dy}{dx} = 0$

$m = \frac{dy}{dx} = -\frac{x - 5}{y + 1}$

At point P we have that x = 10, y = -1, hence:

$m = -\frac{15}{0}$

Undefined slope, hence the tangent line is x = -1.

More can be learned about linear functions at https://brainly.com/question/24808124

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