Precalculus Help: Find the Equation of a Circle Tangent to a Line

[JeNNeHJo]

I was wondering if anyone could help me with this problem

A circle is tanget to line 2x-y+1=0, at point (2, 5), and the center point is on line, x+y=9. Determine the equation (in general form) of the circle.

Normally I can do this sort of problem but I am having a hard time with this one. I don't know how to determine the center point or radius...frustrating..


Thanks, Jennifer

 

[NeutronStar]

I was wondering if anyone could help me with this problem

A circle is tanget to line 2x-y+1=0, at point (2, 5), and the center point is on line, x+y=9. Determine the equation (in general form) of the circle.

Normally I can do this sort of problem but I am having a hard time with this one. I don't know how to determine the center point or radius...frustrating..


Thanks, Jennifer

This might be wrong because I'm basically an idiot, but here's what I'd do,…

Write an equation for a line that is orthogonal to 2x-y+1=0 and also passes through point (2,5).

Then solve for where that line and x+y=9 cross. That point must be the center of the circle.

The radius of the circle is the distance between those two points and the rest is history, … Er,.. I mean, mathematics.

I think that'll do it, but I'm sure some real mathematicians will come along and correct me if I'm wrong.

 

[JasonRox]

This might be wrong because I'm basically an idiot, but here's what I'd do,…

Write an equation for a line that is orthogonal to 2x-y+1=0 and also passes through point (2,5).

Then solve for where that line and x+y=9 cross. That point must be the center of the circle.

The radius of the circle is the distance between those two points and the rest is history, … Er,.. I mean, mathematics.

I think that'll do it, but I'm sure some real mathematicians will come along and correct me if I'm wrong.

That's what I would've done.

 

[anniel]

hello,

i just starting taking classes for pre-cal... haven't taken classes in yrs... besides the calculator and the textbook - what else can i buy to help me with this class? any tools?? (besides a tutor)

Thanks in advance!

A