Question 8: If x and y are connected parametrically by the equation, without eliminating the parameter, find. x = a(cost + logtan t/2) y= a sin t
Class 12 - Math - Continuity and Differentiability
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here x = a[cost+logtant/2] and y = a sint
dx/dt = a[-sint + 1/tant/2.(sec²t/2).1/2]
= a[-sint + cot t/2/2sint/2.cos²t/2]
= a[-sint+1/sint] = a[-sin²t+1/sint]=acos²t/sint
and y = asint => dy/dt = a cost
dy/dx = (dy/dt)/dx/dt = acost.sint/acos²t = tan t
At t = π/4 , dy/dt = tanπ/4 = 1
dx/dt = a[-sint + 1/tant/2.(sec²t/2).1/2]
= a[-sint + cot t/2/2sint/2.cos²t/2]
= a[-sint+1/sint] = a[-sin²t+1/sint]=acos²t/sint
and y = asint => dy/dt = a cost
dy/dx = (dy/dt)/dx/dt = acost.sint/acos²t = tan t
At t = π/4 , dy/dt = tanπ/4 = 1
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