Question

Write the equation of the line that is tangent to the circle (x + 6)2 + (y + 4)2 = 25 at the point (-9, -8).

Answer 1

define the slope of the line that is between the center and the stated point

Answer 2

then perp it by flipping and negating it

a/b perps to -b/a

Answer 3

then attach that perped slope to the stated point in your favorite line equation format

Answer 4

Could you explain that a little differently?

Answer 5

do you know how to define the slope between 2 points?

Answer 6

I'm trying to recall but it's been awhile. can you remind me?

Answer 7

change in y over change in x\[\frac{\Delta y}{\Delta x}=\frac{y_o-y_1}{x_o-x_1}\]

Answer 8

Okay...

Answer 9

-4--8 = 4
-6--9 = 3

Answer 10

the tangent to a circle is 90 degrees (perpendicular) to the slope of the radius ...

Answer 11

Right

Answer 12

perp slopes have the property that their product is -1:
\[\frac{4}{3}*\frac{y'}{x'}=-1\]
\[\frac 34\frac{4}{3}*\frac{y'}{x'}=-1*\frac 34\]
\[\frac{y'}{x'}=-\frac 34\]

Answer 13

now, given a point (a,b) and a slope (m), we can define the equation of a line as:\[y=m(x-a)+b\]

Answer 14

W

Answer 15

Where did the 'a' come from?

Answer 16

in order to make a setup as generic as possible; you use placeholder (letters, variables, etc) to establish a format with

Answer 17

the generic point (a,b) is made specific by the specific point (-9,-8)

Answer 18

Okay okay sorry I knew that

Answer 19

:)

Answer 20

Thank you yet again