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anonymous
 one year ago
By finding the points of intersection, show that the line through (0,5) and (3,9) is tangent to the circle x*2+y^2=9
anonymous
 one year ago
By finding the points of intersection, show that the line through (0,5) and (3,9) is tangent to the circle x*2+y^2=9

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you got the equation for the line?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thats all the question give

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok let me rephrase the question can you find the equation for the line?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1443226608217:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so now to find the point of intersection replace \(y\) in \(x^2+y^2=9\) by \(\frac{4}{3}x+5\) and solve \[x^2+(\frac{4}{3}x+5)^2=9\] and see that there is only one solution to that quadratic

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0x^2+(16/9)x^2+(40/3)x+25=9 (25/9)x^2 + (40/3)x=16

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0should get \[(25 x^2)/9+(40 x)/3+25 = 9\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh yeah, what you got

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0multiply both sides by 9

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[25x^2+120x+144x=0\] which , by some miracle , is a perfect square

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[(5x+12)^2=0\\ x=\frac{12}{5}\] is the only solution

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0typo there, i meant \[25x^2+120x+144=0\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok so thats how we show that the line through the given points is tangent to the circle?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0x^2+y^2=9 12/5+y^2=9 y^2=57/5 y=sq.rt (285)/5

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0this\[25x^2+120x+144=0\]s the quadratic equation you get

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the fact that it has one solution (not 2, not 0) is what tells you that the line is tangent to the graph

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok and if it had 2 solutions then its not tangent to the graph?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes it would cut the circle twice

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and if you had no solutions, it would not cross the circle at all
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