formula for line tangent to circle x^2 - 8x + y^2 + 10y = 0

[chelser13]

find a formula for the line y=mx+b. the line is tangent to a circle at the origin. the circle formula is x^2-8x+y^2+10y=0 .

so i'm trying to find another point for the line so i can figure out the slope thus finding the formula. i have found that the circle's midpoint is at (4,-5). but i'm stuck after that point

Thanks

 

[tkhunny]

Re: formula for line using a circle

y = mx + b

Tangent AT the Origin

0 = m(0) + b ==> b = 0

y = mx

Another point would be nice, but you do not necessarily need one. You could use a slope.

Here's one way.

We have two points of a radius of the circle (4,-5) amd (0.0). What is the slope of the line connecting these?

What is the slope of a line PERPENDICULAR to this radius?