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If x=asin2t(1+cos2t) and y=bcos2t(1-cos2...

If `x=asin2t(1+cos2t)` and `y=bcos2t(1-cos2t),` show that at `pi/4,(dy)/(dx)=b/adot`

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`x = asin2t(1+cos2t)`
`:. dx/dt = a[sin2t(-2sin2t)+(1+cos2t)(2cos2t)] = 2a[-sin^2 2t + cos^2 2t +cos2t]`
`=>dx/dt = 2a[cos 4t + cos 2t]`
`y = bcos2t(1-cos2t)`
`:. dy/dt = b[cos2t(2sin2t)+(1-cos2t)(-2sin2t)]`
`=>dy/dt = b[2cos2tsin2t-2sin2t+2sin2tcos2t]` `=>dy/dt = 2b(sin4t - sin2t)`
Now, `dy/dx = (dy/dt)/(dx/dt) = (b(sin4t - sin2t))/(a(cos4t+cos2t))`
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