HSC Mathematics Marathon (2 Viewers)

hscishard

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That method sounds much better.
First you'd show that the triangles are similar. I got corresp angles and 90 = 90.
Then you find the side lengths of each triangle. It isn't hard, just use pythag. And then yea
I can't draw up a diagram unfortunately..
 
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deterministic

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diagram.jpg
refer to attached diagram:
AP is a line parallel to x axis
You should be able to find X from the equation of the normal.
noting that PAY and OXY are similar triangles, use the ratios of sides to get:
Noting
OX= x coordinate of X
AP= x coordinate of P

 
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I know how to sketch the locus. But how do you find the exact equation of the locus?
Use basic geometry. The locus is a circle, contruct a triangle joining the centre, (0,1) and (0,-1) and make a chocolate cake. The length of the base is obvious (2), the angle subtended at the centre is twice the angle at the circumference (pi/2). Now find the height of the circle to get the coordinates of the centre then find the radius. The cake is a lie.
 

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