Question

Write the equation of the line that is tangent to the circle (x – 2)2 + (y – 4)2 = 289, at the point (-15, 4).
a. y=4
b. x=-15
c. x=4
d. y=-15

Answer 1

not 100% sure, but I'm guessing you're not familiar with calculus right?

Answer 2

especially the concept of derivatives

Answer 3

No. Is that calculus?

Answer 4

yes, seems odd how they can ask you this question when you should know about derivatives

luckily there's a shortcut

Answer 5

the center is (2,4)

the point on the circle is (-15, 4)

so the slope of the line through these two points is


m = (y2-y1)/(x2-x1)


m = (4-4)/(-15-2)


m = 0/(-17)


m = 0

Answer 6

so this means that the line connecting the center to this point is a horizontal line

Answer 7

okay.

Answer 8

this must mean that the tangent line is a vertical line (because it makes a right angle with the radius at this point)

Answer 9

the x coordinate of the point (-15, 4) is x = -15

so the equation of the vertical line is x = -15

Answer 10

if something isn't clicking, drawing it out may help

Answer 11

Your a life saver. Thank you for all that. And that's a good idea.

Answer 12

glad to be of help