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# aea question watch

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1. Could someone please help me with this. Am I supposed to find the turning points and find the distance between them and the origin...

Thanks,

Varun
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2. turning points?
3. it's a circle and you can draw it to see how it works. Shortest and longest distance can see from the line joining O with the centre of the circle
4. maximum and minimum points...
6. ah ok (x - 3) ^ 2 + (y + 4 ) ^ 2 = 49 ?

a center 3,-4 with a radius 7 or something , havent done much of C2 yet
7. mmm.
8. 2 and 12...right?

9. x²+y²-6x+8y=24
(x-3)²+(y+4)²-9-16=24
(x-3)²+(y+4)² = 49

Length of radius = 7 units
Centre of circle = (3,-4)

Line passing through (3,-4) and origin (0,0)

y - 0 = -3/4(x-0)
y = -3x/4

Now sub this equation into x²+y²-6x+8y=24
x²+(-3x/4)²-6x+8(-3x/4) = 24
x²+9x²/16-6x-24x/4=24
x²+3x²/4-6x-6x=24
x²+3x²/4-12x=24
4x²+3x²-48x=96
7x²-48x-96=0
(7x+12)(x-8) = 0
x = -12/7 or 8

y = -3(-12/7)/4 = 36/28 = 9/7
y = -3(8)/4 = -24/4 = -6

(-12/7,9/7),(8,-6)
10. shortest distance: r ( radius) - ( 3^2 +4^2)^(1/2) =7-5=2
greatest distance: 5 + 7 = 12
11. cool

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Updated: November 18, 2005
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