Find all points having an x-coordinate of 1 whose distance from the point (-2,6) is 5

Answer 1

Hi Kimberly,

The general equation for a circle (all the points that are a particular distance away from a given point) is:

(x-x₀)² + (y-y₀)² = r²

where (x₀,y₀) is the center of the circle, and r is the radius of the circle.

In this case, we know that the center of the circle is (-2,6), the radius of the circle is 5, and we are only concerned with the points on that circle that have an x coordinate of 1. That makes our equation:

(1-(-2))² + (y-6)² = 5²

(1+2)² + (y² - 12y + 36) = 25

3² + y² - 12y + 36 = 25

y² - 12y + 45 = 25

y² - 12y + 20 = 0

(y - 2) (y -10) = 0

So the y-values corresponding to an x-value of 1 are:

y = 2 or y = 10

The solutions would be (1,2) and (1,10).

I hope this helps!

Andy