# Thread: Does anybody remember this equation?

1. ## Does anybody remember this equation?

It's a equation for finding all tangent lines to a circle when the point isn't on the circle itself. I think I remember that it was
d=m(x)+b-(y)/√1+m^2

But I can't remember if the x and y are in the correct place.

Edit- Let me show an example. Find the equation of all tangent lines that can be drawn from the point (5,0) to the circle (x-0)^2+(y-0)^2=9.

First I find the line equation.
y-0=m(x-5)
y=m(x-5)+0
y=mx-5m+0

Then I plug this into the equation, note I can only do this one because the center is at the origin because I still can't remember if the x or y are in the correct place but since they are both 0, it doesn't matter for me.
3= m(0)-5m+0-(0)/√1+m^2

9= 25m^2/1+m^2

9+9m^2=25m^2
0=14m^2-9

Uhhh then I blank out here... So I guess I need help solving it and remembering the equation correctly...

2. Originally Posted by C.C
It's a equation for finding all tangent lines to a circle when the point isn't on the circle itself. I think I remember that it was
d=m(x)+b-(y)/√1+m^2

But I can't remember if the x and y are in the correct place.

Edit- Let me show an example. Find the equation of all tangent lines that can be drawn from the point (5,0) to the circle (x-0)^2+(y-0)^2=9.

First I find the line equation.
y-0=m(x-5)
y=m(x-5)+0
y=mx-5m+0

Then I plug this into the equation, note I can only do this one because the center is at the origin because I still can't remember if the x or y are in the correct place but since they are both 0, it doesn't matter for me.
3= m(0)-5m+0-(0)/√1+m^2

9= 25m^2/1+m^2

9+9m^2=25m^2
0=14m^2-9

Uhhh then I blank out here... So I guess I need help solving it and remembering the equation correctly...
I'll take over here: 9+9m^2=25m^2

$\displaystyle 9+9m^2=25m^2~\implies~9=\bold{{\color{red}16}}m^2~ \implies~m^2=\dfrac9{16}~\implies~|m|=\dfrac34$

Seems to me a fairly nice result.