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Old 22nd March 2013, 09:52 PM   #1 (permalink)
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Maths H2 Qn

Find the equation of the asymptotes of the hyperbola 4x^2-24x-9y^2+36y=36. Hence sketch the hyperbola, stating clearly the asymptotes. (i can do this part)

Hence find the range of values of k, such that the equation
4x^2-24x-9(kx+4)^2+36(kx+4)-36=0
has not real roots.how do this part?

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Old 23rd March 2013, 12:48 AM   #2 (permalink)
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Re: Maths H2 Qn

From the first part you get the asymptotes y=-(2/3)x+4 and y=(2/3)x. Notice that k cannot be greater than -2/3 or else y=kx+4 will cut the hyperbola and you will get real roots, so k≤-2/3.

Edit: For visualisation purposes...

You know that you have to graph y=kx+4 and you need values of k such that y=kx+4 doesn't cut the hyperbola.

Notice that y=kx+4 cuts the y-axis at 4, which is the same y-intercept as the asymptote y=-(2/3)x+4. So you know that k can be equal to -2/3.

Increasing k would turn the line y=kx+4 counter-clockwise pivoting the point (0,4) which would make the line cut the hyperbola and you don't want that.

But decreasing k would turn the line clockwise, which you can do, so k≤-2/3.

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Last edited by Betakuwe; 23rd March 2013 at 01:07 AM.
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Old 23rd March 2013, 07:43 AM   #3 (permalink)
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Re: Maths H2 Qn

Wah zachary same cohort as me? J1?

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Old 23rd March 2013, 11:07 AM   #4 (permalink)
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Originally Posted by EightyOne View Post
Wah zachary same cohort as me? J1?
If I remember he is J2.

Sent from my Xperia Z

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