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# C4 help-coordinate geometry in (x,y) plane watch

1. im trying to prepare for tomorrows exam and its not going well

can anyone help me with this question-it would be much appreciated!

a curve has parametric equations x=4sinø, y=3sin2ø

show that the cartesian eqn of the curve can be written in the form y²=ax²(16-x²), where a is a constant to be found
2. from that you can see that x/4 = sinø

also from y= 3sin2ø = 6sinøcosø = 6x/4*cosø

you know sin² + cos²=1 then cosø= √(1- sin²ø) = √(1-x²/16)

then y = 3x/2*√(1- x²/16)
y² = 9x²/4*(1- x²/16)
y² = 9x²/4*1/16(16-x²)
y² = 9x²/64*(16-x²)

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Updated: June 14, 2006
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