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laxieqv
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In the xy plane, the diameter of one circle is 4 (the Updated on: 10 Jan 2006, 23:52
Originally posted by laxieqv on 10 Jan 2006, 23:31.
Last edited by laxieqv on 10 Jan 2006, 23:52, edited 1 time in total.
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In the xy plane, the diameter of one circle is 4 (the center of this circle is at (0,0)), one line is tangent to the circle at (-sqrt(2), sqrt(2)). What is the slope of this line?

A -1

B 1

C 2

D -2

E sqrt(2)



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In the xy plane, the diameter of one circle is 4 (the 10 Jan 2006, 23:46
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Slope of the line passing through points (0,0) and (-sqrt(2), sqrt(2)), m = -sqrt(2)/sqrt(2) = -1

So slope of perpendicular line = -1/m = 1
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In the xy plane, the diameter of one circle is 4 (the 10 Jan 2006, 23:54
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Good problem. Got it once I remembered the "negative" inverse slope trick.
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In the xy plane, the diameter of one circle is 4 (the 11 Jan 2006, 00:00
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laxieqv
In the xy plane, the diameter of one circle is 4 (the center of this circle is at (0,0)), one line is tangent to the circle at (-sqrt(2), sqrt(2)). What is the slope of this line?

A -1
B 1
C 2
D -2
E sqrt(2)
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slope of the line from (-sqrt(2), sqrt(2)) to th eorigin is -1. the slope of the line that is perpendicular to the line with -1 slope is 1.
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laxieqv
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In the xy plane, the diameter of one circle is 4 (the 13 Jan 2006, 08:04
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buddies, you will hit the 7XX range~ :wink:
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In the xy plane, the diameter of one circle is 4 (the 13 Jan 2006, 08:48
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Lol, could you super geniuses slow down for a sec and explain this trick to me ? Im not sure when the perpendicular parts comes into play.

Thanks !
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laxieqv
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In the xy plane, the diameter of one circle is 4 (the 16 Jan 2006, 04:13
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pmenon
Lol, could you super geniuses slow down for a sec and explain this trick to me ? Im not sure when the perpendicular parts comes into play.

Thanks !
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Yeah, the trick is that the tangent line must be perpendicular to the radius drawn from the origin of the circle to the tangent point of the circle and the line. Why? If you want to know, you can refer to my proving :)
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proof.doc [147 KiB]
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allabout
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In the xy plane, the diameter of one circle is 4 (the 16 Jan 2006, 07:35
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Alternatively

The tangent and the circle have only one point in common P(-sqrt2, sqrt2).

The line between O and P has to be perpendicular to T (tangent), because otherwise T wouldn't be a tangent, but a secant.



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This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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