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Over9000

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over9000 questions thread
« on: March 07, 2009, 05:03:31 pm »
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This is a question from 2007 specialist SAC we got for revision that im not sure how to do.
By setting up a suitable quadratic equation, show that the line is a tangent to the hyperbola
If they are tangents, what can you say about them? I'm not sure about what the first step should be
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TrueTears

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Re: over9000 questions thread
« Reply #1 on: March 07, 2009, 05:05:41 pm »
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I shall attempt this question
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Re: over9000 questions thread
« Reply #2 on: March 07, 2009, 05:07:06 pm »
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Ok, first step would be subbing in into the hyperbola and you will end up with a quadratic. Then find the discriminant of that quadratic and it should = 0. Hence it touches (ie tangent) to the ellipse
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Over9000

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Re: over9000 questions thread
« Reply #3 on: March 07, 2009, 05:14:09 pm »
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What is the discriminant formula, sorry I forgot it
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Re: over9000 questions thread
« Reply #4 on: March 07, 2009, 05:14:49 pm »
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it's just the thing under the square root of quadratic general formula
« Last Edit: March 07, 2009, 05:37:09 pm by TrueTears »
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Over9000

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Re: over9000 questions thread
« Reply #5 on: March 07, 2009, 05:23:09 pm »
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still having trouble, could you maybe do a few steps for me, the math is quite hard
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Re: over9000 questions thread
« Reply #6 on: March 07, 2009, 05:24:12 pm »
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ok so...


expanding this ( remember you can use a calc for your SAC) yields

Try now... and if you can't get it, ask me again
« Last Edit: March 07, 2009, 06:36:08 pm by TrueTears »
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Over9000

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Re: over9000 questions thread
« Reply #7 on: March 07, 2009, 05:27:44 pm »
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k thanks, that should help enough, hopefully
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Re: over9000 questions thread
« Reply #8 on: March 07, 2009, 05:31:43 pm »
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I get
so
but that gives me 200
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Re: over9000 questions thread
« Reply #9 on: March 07, 2009, 05:34:29 pm »
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you shouldn't...

So from that step i left off,

with more simplifying you get

subbing this in the yields



because so they only touch.

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Over9000

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Re: over9000 questions thread
« Reply #10 on: March 07, 2009, 05:36:14 pm »
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lol, i used that, so should it be instead
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Re: over9000 questions thread
« Reply #11 on: March 07, 2009, 05:56:27 pm »
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Having trouble with this question, adddon from the previous
The line passes through the point B(3,2). By referring to the sketch of , state the equation of the other tangent to the hyperbola that passes through B, and state the the coordinates of the point of intersection , C, of this tangent with the hyperbola.
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Re: over9000 questions thread
« Reply #12 on: March 07, 2009, 05:59:22 pm »
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The only other tangent would be x=3, basically you have visualise this on the graph as there is not enough information to work it out analytically.

(Thank kamil and /0 for explaining this to me)
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Over9000

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Re: over9000 questions thread
« Reply #13 on: March 07, 2009, 06:02:22 pm »
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Ok thanks, that explains why I couldn't find the answer with calculations.
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Over9000

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Re: over9000 questions thread
« Reply #14 on: March 07, 2009, 07:19:13 pm »
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Another question
The point P (3cosx,2sinx),, is a point on the ellipse . S is the point .
The line segment SP is extended to the point Q where P is between S and Q and SQ=3SP
Calculate the coordinates of Q (in terms of x)
« Last Edit: March 07, 2009, 07:33:50 pm by Over9000 »
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Gundam 00 is SOOOOOOOOHHHHHHHHH GOOOOOOOOOOODDDDDDDDDDDD I cleaned my room

VCE 200n(where n is an element of y): Banter 3/4, Swagger 3/4, Fresh 3/4, Fly 3/4
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