Find the equations of the tangent and the normal to the following curves at the indicated points.(i) x = θ + sinθ, y = 1 + cosθ at θ = π2(ii) x=2 at21+t2, y=2 at31+t2at t=12(iii) x = at2, y = 2at at t = 1(iv) x = asect, y = btant at t(v) x = a(θ + sinθ), y = a(1 − cosθ) at θ(vi) x = 3cosθ − cos3θ, y = 3sinθ − sin3θ [NCERT EXEMPLAR]

Find the equations of the tangent and the normal to the following curv

1.	Find the equations of the tangent and the normal to the following curves at the indicated points.(i) x = θ + sinθ, y = 1 + cosθ at θ = π2(ii) x=2 at21+t2, y=2 at31+t2at t=12(iii) x = at2, y = 2at at t = 1(iv) x = asect, y = btant at t(v) x = a(θ + sinθ), y = a(1 − cosθ) at θ(vi) x = 3cosθ − cos3θ, y = 3sinθ − sin3θ [NCERT EXEMPLAR]
Answer» Find the equations of the tangent and the normal to the following curves at the indicated points. (i) x = θ + sinθ, y = 1 + cosθ at θ = $\frac{π}{2}$ (ii) $x = \frac{2 a t^{2}}{1 + t^{2}}, y = \frac{2 a t^{3}}{1 + t^{2}} at t = \frac{1}{2}$ (iii) x = at², y = 2at at t = 1 (iv) x = asect, y = btant at t (v) x = a(θ + sinθ), y = a(1 − cosθ) at θ (vi) x = 3cosθ − cos³θ, y = 3sinθ − sin³θ [NCERT EXEMPLAR]