Please help with a ‘points of intersection’ math(s) problem?
QUESTION:
Find the points of intersection of the line y = 5x + 13 with the circle x^2 + y^2 = 13.
I’m not really sure how to approach this one. I have tried to solve it like a simultaneous equation by using substitution:
x^2 + (5x +13)^2 = 13
This eventually leads to the quadratic:
26x^2 + 130x + 156 = 0
I’m not even sure that what I am doing is even remotely correct but if by some chance it is I am still stumped when I get to this stage.
Please help!!
Thanks for the response…it’s good to know I was on the right track!
Would someone please help me apply the formula x = -b ± sq.rt 4ac
—————-
2a
to the above quadratic as I can;t seem to get it right
your approach is correct
26x^2 + 130x + 156 = 0 gives x = -3 and x = -2
sub these into y to give
y = -2 and y = 3
so the intersections are at, (-3,-2) and (-2,+3)
please check out the links, I think you’ll be surprised if you haven’t seen wolframalpha before…
http://www.wolframalpha.com/input/?i=solve[y+%3D+5x+%2B+13,+x^2+%2B+y^2+%3D+13]+for+x+and+y
http://www.wolframalpha.com/input/?i=plot[y+%3D+5x+%2B+13,+x^2+%2B+y^2+%3D+13]+
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