Question

Write the equation of the line that is tangent to the circle x2 + y2 = 169 at the point (-5, 12).

Answer 1

Where is center of the circle?
Distance of point (-5,12) is one radius from center.
Draw this radius and
Make an equation for the line, y = km + b
Tangent is perpendicular to the line, so use
K1 * k2 = -1.

Answer 2

I got -5/12x+169

Answer 3

Wait 5/12x

Answer 4

For radius k = -5/12. It is descending line.
K for tangent should be positive

Answer 5

No it's 5/12
It doesn't have a negative

Answer 6

-5/12 * k =-1
K for tangent is 12/5, right?

Answer 7

I really don't know
all I know is that it doesn't have a negative

Answer 8

K = -1 /(-5:12) = 12/5

Answer 9

Is it 12/5x+12/169 ?

Answer 10

Then use y -y0 = k(x- x0)

Remember multiply both : kx and k* (-12)

Answer 11

(12/5) x is right

Answer 12

y - (-5) = 12/5 (x -12)
Remember -5 in another side

Answer 13

y=12/5x+12/169

Answer 14

In standard form

Answer 15

Right side is 12/5 x - 12*12 / 5 +5

Last one 5 comes from left side.

Answer 16

Can you conform my answer?

Answer 17

I got y = (12/5) x - 23 4/5

12* 12 = 144

-144/ 5 = -28 4/5, then add 5

Answer 18

I got it wrong.

Answer 19

Ok, I think you find the idea.
I suggest you make a good Sketch of this.

Good luck for your studies!

Answer 20

The tangent line is: y = 5/12x + b
Point (-5, 12) is on that tangent line.
12 = 5/12 * (-5) + b
12 = -25/12 + b
b = 12 + 25/12 = (144 + 25)/12 = 169/12

y = 5/12x + 169/12

Answer 21

I got a sign error, when I moved 5 from left to right,
Sorry!

Answer 22

A plot is attached.