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Show that the line $3x-4y=25$ and the circle $x^2+y^2=25$ intersect in two coincident points. What does two coincident points mean?

Paul
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hooray_parsad
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  • "Two coincident points" here means that the line only intersects the circle at one point, that is, two points that "happen to be the same" – Ben Grossmann Feb 23 '14 at 06:25

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If you draw a line through a circle, normally they intersect at two points. The problem is asking you to show that it only intersects at one point. Coincident means "occurring together in space or time", so two possible coincident points are actually one point.

DanielV
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  • plz solve this question – hooray_parsad Feb 23 '14 at 06:32
  • I did. I wrote the first equation as $y = \frac {3x - 25} 4$ and substituted that $y$ into the second equation. You get a quadratic. Are you familiar with solving quadratic equations? – DanielV Feb 23 '14 at 06:38
  • here I get value of y= -4 and y= -4 and x=3,3 then two coincident points are (3,-4)and(3,-4). – hooray_parsad Feb 23 '14 at 06:49
  • Good, it is the same as my result. You probably want to specifically address the discriminate of the quadratic, $b^2 - 4ac$. The coincidence is a direct result of the discriminate being zero. Can you guess what it looks like when there is only 1 point of intersection? – DanielV Feb 23 '14 at 06:54
  • I think a straight line must pass tangentially. – hooray_parsad Feb 23 '14 at 07:11
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Coincident means same point. That is this line forms a tangent to the circle at some point.

UNM
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Whenever you see the word "coincident", just think "same". Have you ever graphed / analyzed two coincident lines in coordinate geometry? These lines lie exactly on top of each other, and have equations like $2x - y = 3$ and $y = 2x - 3$. After graphing these lines, only one line should be seen, because both lines are exactly the same. Likewise, coincident points mean that the points lie on top of each other. Only one point can be seen

Anonymous Computer
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