# MATH

posted by .

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 -

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 -

What do you mean?

• MATH -

What do youm mean?

## Respond to this Question

 First Name School Subject Your Answer

## Similar Questions

1. ### help!

Can you please give me one of them so I cansolve for the other one?
2. ### algebra

how would i find an equation of a line that goes through points(1,6) and (3,10)?
3. ### Algebra

Wrtie an equation of a line passing through (6,10) and (6,-6 y= mx + b Put in the first set of points: 10=6m + b Do the same for the second point. Then, you have two equations, two unknowns. Solve by substitution.
4. ### maths pleaaaase

The point X and Y are 8cm apart Draw a scale drawing of the diagram and draw the locus of points that are equidistant from both points X and Y what do they mean by equidistant Equidistant means the same distance. I'm not a teacher, …
5. ### Algebra

Can someone check my answers? 1. Write the equation of the line that passes through point (–2, 3) with a slope of –4. Answer: y = -4x - 5 2. Find the slope and y-intercept. x = –8 Answer: Slope: undefined; y-intercept: none 3.
6. ### Algebra

Consider the points (3, –1) and (9, 2). (a) State the midpoint of the line segment with the given endpoints. (b) Find the distance between the points. Show some work. Give the exact answer (involving a radical), and also an approximation …
7. ### intermediate algebra

Write the equation of the line: The points are at (-8,-6) and (0,0). The line passing through these two points has a y-intercept of 0 since it passes through the origin. The slope is -6-0/-8-0=3/4 How would I finish this?
8. ### Math - Quadratics & Analytical Geometry

I have a test tomorrow with a few sample questions that are expected to be on the test that I do not know how to properly do. 1)Find the slope intercept equation of the line passing through the intersection of the lines 2x-4y=1 & 3x+4y=4 …
9. ### Math -Quadratics Help!

I have a test tomorrow with a few sample questions that are expected to be on the test that I do not know how to properly do. 1)Find the slope intercept equation of the line passing through the intersection of the lines 2x-4y=1 & 3x+4y=4 …
10. ### Math Question

Laura was given two points (3,-2) and (-2,4) and was asked to create an equation that represents the line that passes through these points. Write two equations that she could use.

More Similar Questions