Question

please check my answers--> consider the circle whose equation is (x+5)^2 + (y-4)^2 = 169.
a. find the coordinates of the points of intersection of the circle with the y axis. b. find the coordinates of the point(s) of intersection of the circle with the line x=8.

Answer 1

I was a little confused because I felt like they were asking for the same thing on both of the questions, but I got..
a. (8,4) & (-5,17)
b. (8,4) & (8,-4)

Answer 2

to find the coordinates of the points of intersection of the circle with the y axis, you need to set x = 0 and plug it in to the circle equation to find y, you will get two y values and therefore the points are (0,y₁) and (0,y₂)

Answer 3

for b, there is only 1 point of intersection of the circle with line x = 8

Answer 4

exraven is correct. Put x=0 into the equation and solve for y; you solutions will be (0,y1), (0,y2).

Then put x=8 into the equation to get the point of intersection with x=8 (note that the radius is 13, and the x coordinate of the center is -5; that means the circle just touches the vertical line x=8).

Answer 5

I guess I don't type quite fast enough....LOL

Answer 6

If you look at the numbers a little bit, you probably get (0,16) and (0,-8). (Not magic, and not even a calculator. It's a 5-12-13 triangle; that Pythagorean triple shows up in math books often enough that you might know it by now....) and the intersection of the circle and x=8 is at (8,4) (same y coordinate as the center of the circle....).

Answer 7

How did you know to set x = 0 to solve for y? I found 2 points of intersection for b..

Answer 8

I got (0,-8) for x=0

Answer 9

zoe11: draw the picture carefully. The equation represents a circle of radius thirteen centered at (-5,4) I think you'll find the points in my post above.

Answer 10

By the way, in response to your earlier question, we set x to zero when we want to consider anything on the y axis, since the position of the y axis is x=0.