Question

Write the equation of the line that is tangent to the circle 169=x^2+y^2 at the point (-12,5).

Answer 1

Can you calculate the first derivative of the equation for the circle?

Answer 2

To be honest, I have no clue what that is lol.

Answer 3

np. y' = +-x/sqrt(169-x^2)^(1/2)

Answer 4

You will be using "+" since this a point in the second quadrant, so we just put -12 for x in this derivative equation. That is, to get the slope for the tangent line. BTW are you in calculus?

Answer 5

No, I'm in Algebra2.

Answer 6

So, slope is +1/5. Okay, we need to do this by another method.

Answer 7

Do I need to know the center?

Answer 8

We can't expect you to use methods not available to you at this point. So, this is a circle a tthe origin, point (0, 0). Yes, you need the center. But now we know it. It is implied by the form of the equation.

Answer 9

So, the next thing we have to do, after identifying the center which is (0, 0), is get the slope of the line from (0, 0) to (-12, 5). Do you know how to do that?

Answer 10

Do I use slope formula?

Answer 11

\[\frac{ y _{1} - y _{2} }{ x _{1} - x _{2} } = m\] where m is the slope. And (x1, y1) and (x2, y2) are 2 points on the line. And we know of 2 points on that line, so you would be able to calculate the slope. Can you do this substitution and show me the slope?

Answer 12

12/5?

Answer 13

12/5 will be the slope of the tangent line, which is the second step of this problem. The slope of the line between (0, 0) and (-12, 5) is the negative reciprocal or -5/12. Your teacher must have given you a combined step. Anyway, the tangent line slope is 12/5. And now you can use the point-slope formula.

Answer 14

The first part of the equation is "y=12/5x" correct?

Answer 15

Well, I'm not sure what "first part" means here, but I believe you are on the right track, because the slope of the tangent line is 12/5, so you have that part identified correctly, if that is what you mean. I'll write out the point-slope formula. It's similar to the other formula I wrote.

Answer 16

\[\frac{ y - y _{1} }{ x - x _{1} } = m\] or, putting th denominator over on the right side, we have\[y - y _{1} = m(x - x _{1})\]

Answer 17

You know m is 12/5 and you have the point (-12, 5) for (x1, y1), so you can now just substitute.

Answer 18

I got y=12/5x+169/5

Answer 19

Yes! Very good!

Answer 20

Thank you!