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At what point does the graph of 3x+4y=15 intersect the graph of x^2+y^2=9? Express any non-integer coordinate as a common fraction.

Aug 7, 2020

#1
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Well it is a line intersecting with a circle so it could be 0,1 or 2 times, but you are already told that there is only one point so the line must be a tangent.

If you want to check I would use the perpendicular distance formula fro a point to a line.  I have done that and the distance is indeed 3.

And three is the radius of the circle so the line is a tangent to the circle (only 1 point of intersection)

You could just solve the 2 simultaneously.  That is the normal way

Or you could say that the equation of the line is

$$3x+4y=15\\ 3x=15-4y\\ x=\frac{15-4y}{3}\\ \text{So a point on the line is } (\frac{15-4y}{3},y)$$

use the normal distance formula and put the distance =3   solve for y then solve for x

Aug 7, 2020
#2
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At what point does the graph of 3x+4y=15 intersect the graph of x^2+y^2=9? Express any non-integer coordinate as a common fraction.   Aug 7, 2020