Question

Sketch the circle of radius 2 centered at (3, -3) and the line L with equation y = 2x + 2. Find the coordinates of all the points on the circle where the tangent line is perpendicular to L.

Answer 1

Answer:

Please refer to the attachment below.

Step-by-step explanation:

Please refer to the attachment below for explanation.

Answer 2

The points on the circle where the tangent line is perpendicular to L are $(x,y) = (3.88, -1.204)$ and $(x,y) = (2,092, -4.782)$, respectively.

The circle of radius 2 centered at $(x,y) = (3, -3)$ is represented by $(x-3)^{2}+(y+3)^{2} = 4$ and the line L is $y = 2\cdot x + 2$. In this question we must find two points on the circle where tangent lines are perpendicular to L.

We proceed to sketch the circle and the line L and after some iterations we find that the two tangent lines are $y = -\frac{1}{2}\cdot x -3.736$ (red line) and $y = -\frac{1}{2}\cdot x + 0.736$ (black line), whose tangent points are $(x,y) = (3.88, -1.204)$ and $(x,y) = (2,092, -4.782)$.

To learn more on tangent lines, we kindly invite to check this verified question: https://brainly.com/question/6617153