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Preliminary mathematics marathon (1 Viewer)

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Still working on the answer. LOL. Trig ain't my strong point.

Here's a question whilst I work on your one:

i) Find the coordinates of the CENTRE (C) and the RADIUS of the circle x^2+y^2-2x+4y-4=0.

Find the length of the perpendicular from C (Centre) on to the straight line 5x-12y+10=0 and hence prove this line is a tangent to the circle.
 
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After completing the square, you get (x-1)2+(y+2)2=9.

So the centre is C(1,-2) and radius is r=3.

For the second part, you use the perpendicular distance formula to find that it's 3, the same as the radius, so it only touches the circle one, therefore it's a tangent to the circle.
 
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Considering I really need practice at trig equations, especially the t formulas (seeing as my teacher has yet to teach them), I'll post up another:

The point A(a,b) divides the interval from B(3,-2) to C(0,4) in the ratio M:1 internally.
i) Write down the coordinates of the point A in terms of M.
ii) If A lies on the line y=2x+3, determine the value of M and hence find the coordinates of A.
 
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I think that's the equation of the tangent, I got y=x-4...
I see. Anyways,

new question:

The normal and the tangent at P(2,-2) on the curve y = x^3-x^2-6 cuts the x-axis in N and T respectively. Find the area of triangle PNT.
 

hscishard

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New question:

A cubic curve has a minimum point at point (-2,-15), a maximum point at (1,12)
and it cuts the y axis at 5. What is the equation of the cubic?

A good question:)
 

hscishard

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Still working on the answer. LOL. Trig ain't my strong point.

Here's a question whilst I work on your one:

i) Find the coordinates of the CENTRE (C) and the RADIUS of the circle x^2+y^2-2x+4y-4=0.

Find the length of the perpendicular from C (Centre) on to the straight line 5x-12y+10=0 and hence prove this line is a tangent to the circle.
5(1) -12(-2)+10
--------------------
root 5
=39/root5

Does no equal to 3, hence not a tangent.
WTF. What did I do wrong?

OOOO used coodinates with the sqaure bit.

39/ root 25 +144
= 39/root 169
=39/13
=3. :) damn, been a long time since i've used that forumla
 

smileygirl

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5(1) -12(-2)+10
--------------------
root 5
=39/root5

Does no equal to 3, hence not a tangent.
WTF. What did I do wrong?

OOOO used coodinates with the sqaure bit.

39/ root 25 +144
= 39/root 169
=39/13
=3. :) damn, been a long time since i've used that forumla
I'd never actually seen that formula before till now. But I get it :)
 

AAEldar

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Post some questions that I can answer! :(

Haven't done any of this stuff yet >.< Haha.
 

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