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Question
Find the slope of the tangent to the following curves at the respective given points.
x = a cos3t, y = b sin3t at t = `pi/2`
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Solution
x = a cos3t, y = b sin3t
Differenriating w.r.t. ‘t’
`("d"x)/("dt"` = – 3a cos2t sin t
`("d"y)/("dt"` = 3b sin2t sin t
`("d"y)/("d"x) = (("d"y)/("dt"))/(("d"x)/("dt"))`
= `(3"b" sin^2 "t" cos "t")/(-3"a" cos^2"t" sin"t"`
= `- "b"/"a" sin"t"/cos"t"`
= `- "b"/"a" tan "t"`
Slope of the tangent `(("d"y)/("d"x))_(("t" = pi/2))`
= `- "b"/"a" tan i/2 = oo`
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