eq. of lines tangent to circles

G

Guest

Guest
I should remember how to do this because its a review, but I can't. HELP!

The equation of the circle= x^2+y^2-6x-8y=0
The center point= (3,4) and the radius=5

The first question is: Find an equation of the line tangent to the circle at the point (0,0).
The second question is: Find an equation of the line tangent to the circle at the point (6,0).
The third question is: Where do the tangent lines intersect?

I should be able to get the third once I have the answers to 1 & 2. I am so stressed out, I have stared at this and can't remember how to do it. :x
 
Have you covered implicit differentiation, or are you supposed to work from the fact that the tangents are perpendicular to the radii?

Eliz.
 
If you have 2 line equations their point of intersection can be found by solving the equations!!

When we "solve" a quadratic equation we find a value that satisfies both the equations. In this case, it means that both lines will pass through that point which automatically means that the two lines intersect at that point!
 
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