Radius of a circle.

Question

Consider a circle centered at (-3,2) of radius 3.

a) Draw this circle on the xy-plane and label it carefully. Use your picture to

determine the number of solutions to x = −5.

b) What point(s) lie on that circle and the line y = 1?

I did draw the circle on the plane, but I am confused about how to proceed.

Answer 1

I am unable to produce a graph for you but it should be very easy to take a piece of graph paper and with the center at (-3,2) draw a circle of radius 3. You will see that the 'top' point of the circle is at (-3,5), the 'bottom' point of is at (-3,-1), the 'right' point is at (0,2) touching the y-axis and the 'left' point is (-6,-2).

The equation of the circle is (x + 3)^2 + (y - 2)^2 = 9, (9 being the radius squared.)

Now draw the vertical line x = -5 through the circle. You can see that it intersects the circle in 2 places.

To find the y coordinates of the 2 points substitute x = -5 into the equation and solve for y. You will get 2 solutions.

Now draw the horizontal line y = 1 through the circle. Again you will see that it intersects the circle 2 places.

To find the x coordinates of the 2 points substitute y = 1 into the equation and solve for x. Again you will get 2 solutions.

Answer 2

a) Locate all the points on the circle that have x = -5

b) Draw the line y = 1. At which points on the circle does it intersect?