Posted by **Connie** on Friday, April 25, 2008 at 2:54pm.

two circles whose equations are (x-3)^2+(y-5)^2=25 and (x-7)^2+(y-5)^2=9 intersect in two points. What is the equation of the line passing through these two points?

Can anyone please give me some ideas how to do it without graphing it out? THANKS A LOT!

- MATH -
**Damon**, Friday, April 25, 2008 at 3:32pm
The centers are at (3,5) and at (7,5) along the horizontal line y = 5 and 7-3 = 4 apart

left radius = 5

right radius = 3

so

the points lie on vertical line x = something an equal distance above and below y = 5

so

triangle

base = 4 along y = 5 line

left leg = 5

right leg = 3

let's use law of cosines to find the angle on the left, between the y = 5 line and the long side length 5

3^2 = 5^2 + 4^2 - 2*5*4 cos A

9 = 25 + 16 - 40 cos A

32 = 40 cos A

A = 36.87 degrees

now the distance from x = 3 to our desired vertical line is

5 cos A which is 5 (32/40) = 4

so our line is

x = 3 + 4 = 7

which we could have said earlier seeing that our triangle is

3, 4, 5 and therefore a right triangle

- MATH -
**Jordan**, Friday, April 25, 2008 at 9:32pm
What do you mean?

- MATH -
**Jordan**, Friday, April 25, 2008 at 9:32pm
What do youm mean?

## Answer This Question

## Related Questions

- maths pleaaaase - The point X and Y are 8cm apart Draw a scale drawing of the ...
- algebra - how would i find an equation of a line that goes through points(1,6) ...
- help! - Can you please give me one of them so I cansolve for the other one?...
- Algebra - Can someone check my answers? 1. Write the equation of the line that ...
- Math Question - Laura was given two points (3,-2) and (-2,4) and was asked to ...
- Algebra - Wrtie an equation of a line passing through (6,10) and (6,-6 y= mx + b...
- intermediate algebra - Write the equation of the line: The points are at (-8,-6...
- Math -Quadratics Help! - I have a test tomorrow with a few sample questions that...
- Math - Quadratics & Analytical Geometry - I have a test tomorrow with a few ...
- Algebra - Consider the points (3, –1) and (9, 2). (a) State the midpoint of the ...

More Related Questions