SOLUTION: The circle is tangent to the line 3x-4y=34 at the point (10,-1) and also tangent to the 4x+3y=12 at hte point (3,0)

Algebra ->  Equations -> SOLUTION: The circle is tangent to the line 3x-4y=34 at the point (10,-1) and also tangent to the 4x+3y=12 at hte point (3,0)      Log On


   

Question 1041862: The circle is tangent to the line 3x-4y=34 at the point (10,-1) and also tangent to the 4x+3y=12 at hte point (3,0)
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
This response is very abbreviated and is not a full solution with steps;
(Now filling in some of the parts, not all parts):

-4%2F3 slope and point (10,-1); find equation of this line.
y%2B1=-%284%2F3%29%28x-10%29
y=-4x%2F3%2B40%2F3-1
y=-4x%2F3%2B40%2F3-3%2F3
y=-4x%2F3%2B37%2F3

3%2F4 slope and point (3,0); find equation of this line.
y-0=%283%2F4%29%28x-3%29
y=3x%2F4-9%2F4

What is the intersection point for these two 'found' lines? This is the center of the circle.
-4x%2F3%2B37%2F3=3x%2F4-9%2F4----equating the expressions for y;
37%2F3%2B9%2F4=3x%2F4%2B4x%2F3
12%2A37%2F3%2B12%2A9%2F4=12%2A3x%2F4%2B12%2A4x%2F3
4%2A37%2B3%2A9=9x%2B16x
25x=175
highlight_green%28x=7%29
-
y=3x%2F4-9%2F4
y=3%2A7%2F4-9%2F4
y=21%2F4-9%2F4
y=22%2F4
highlight_green%28y=11%2F2=5%261%2F2%29
-
Center of Circle is ( 7, 5&1/2 )

Do you know how to find the value for the radius?
(Use the Distance Formula...)

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

The circle is tangent to the line 3x-4y=34 at the point (10,-1) and also tangent to the 4x+3y=12 at hte point (3,0)
What do you want? Aren't you supposed to ask a question?

Whatever that may be, the center of the circle is at coordinate point: (7, 3). You need to figure out what you want and how you can get it.

Whatever help we provide on this site, I don't believe mind-reading is one!