Question

Need geometry help. The equation of a circle is (x + 6)2 + (y + 2)2 = 16. The point (-6, 2) is on the circle.

What is the equation of the line that is tangent to the circle at (-6, 2)?

Answer 1

I suppose you mean \((x+ 6)^2 + (y+2)^2 = 16\), correct?

Answer 2

yes

Answer 3

Wouldn't you have to take the derivative to find the slope, then plug the points (-6,2) and your slope into the form

y= mx+b to find the y intercept?

Then rewrite the equation for the tangent line?

Answer 4

I hope you know where you're heading Jhannybean because this is not single variable analysis anymore.

Answer 5

Oh hahaha i was just guessing!! nevermind then :P

Answer 6

Line perpendicular to the line connecting the point and the center that also goes through the given point?

Answer 7

Yesss

Answer 8

The slope is zero at the point so it will just be the line y = 2. But this is only via visual inspection actually proving this is more difficult.

Answer 9

ok cool thanks for the help

Answer 10

omg this is so not to scale :|

Answer 11

maybe that's how it's drawn? :\ not sure...

Answer 12

Probably not, haha, i tried!!

Answer 13

http://www.wolframalpha.com/input/?i=%28x%2B6%29%5E2+%2B+%28y%2B2%29%5E2+%3D+16%3B+y+%3D+2

Answer 14

thanks for trying

Answer 15

Visit the wolfram link for the graph he was trying to draw.

Answer 16

Ohhhhh I see it now!!!

Answer 17

thanks again for helping

Answer 18

I'm not sure how you can prove it formally without multivariable calculus.

Answer 19

Haha.i shall be learning that next semester! :P

Answer 20

Obviously, the picture is THE thing!

Answer 21

How to prove it with analysis? Notice that the circle is a manifold without boundary. We can define the chart \(\alpha(\theta) = (4\cos(\theta) - 6, 4\sin(\theta) - 2)\)
\). Then just consider the tangent space of the chart at the angle corresponding to that point which is going to be \(\pi/2\)

Answer 22

Oh my!

Answer 23

@Alchemista are you done with all math?past multivariable calc? just wondering.

Answer 24

One is never done with all math. INFINITY DON'T YOU KNOW?

Answer 25

lol