## find equation for line passing through pts of intersection

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
testing
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### find equation for line passing through pts of intersection

I have to find an equation for the line that passes through the points of intersection of the circles $x^2+y^2=25$ and $x^2-3x+y^2+y=30$. Can I just subtract and get $-3x+y=5$?

stapel_eliz
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You'd need first to find the slope of that line, in order to answer the question asked. To check your answer, go the long way 'round:

Solve the line equation you got for "y=", and plug this into either of the original equations in place of "y". (I'd use the x2 + y2 = 25: it's simpler.) Solve the resulting quadratic for two values of x, and then back-solve for the corresponding values of y. This will give you the two points of intersection, which you can then plug into the slope formula.

And you can always check your answer by graphing. You can either confirm that the two points are on each circle, or else you can just graph the two circles and the line, and make sure they overlap at the right spots. If you're plugging into a graphing calculator, you'll need to do the circles in two halves, since of course their equations aren't functions.

. . . . .$\mbox{Y1}\, =\, -0.5\, -\, \sqrt{32.5\, -\, \left(\mbox{X}\, -\, 1.5\right)^2$
. . . . .$\mbox{Y2}\, =\, -0.5\, +\, \sqrt{32.5\, -\, \left(\mbox{X}\, -\, 1.5\right)^2$
. . . . .$\mbox{Y3}\,=\, -\sqrt{25\, -\, \mbox{X}^2}$
. . . . .$\mbox{Y4}\,=\, \sqrt{25\, -\, \mbox{X}^2}$
. . . . .$\mbox{Y5}\, =\, 3\mbox{X}\, +\, 5$

Have fun!