Answer:
and
Step-by-step explanation:
We are asked to graph the circle of radius 2 centered at (3,–3) and the line L with equation .
We know that standard form of circle with center at point (h,k) is . Upon substituting our given values, we will get:
Please find the attachment for the graph.
We need to find the points, where, the tangent of circle are perpendicular to L.
We know that slopes of perpendicular lines are negative reciprocal of each other, so slope of tangent line would be negative reciprocal of 2 that is .
We need to find P points on the circle such that the radial line from point (3,–3) to P has a slope equal to 2.
Now, we will substitute this equation in circle equation to solve for x-coordinates of points.
Now, we will use quadratic formula.
We figured our x-coordinates of our required points.
Now, we will substitute these points in equation to find y-coordinates as:
2nd y-coordinate:
Therefore, our required points are and .