+13 \(\)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.
+118667 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
