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- The parametric curve defined by [x = 4t - π · sin(2t) ly = 4 - π· cos(2t) is shown. The curve intersects itself at the point (0,4).Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x=e^(-3t) cos (8t) y = e^-3t sin (8t) z = e^-3t (1,0,1)Obtain the differential equation of the family of plane curves described. 1. All ellipses having its centers at the origin and traverse axis x.
- The equation of the upper semicircle centered at the origin with radius R in parametric form is given byx=Rcost,y=Rsint,where0<t<π.Find the third differential d3y of this function.Obtain the differential equation of the plane curves described. 2. Family of ellipses with center at the origin.Find the 1st and 2nd derivatives of y with respect to x from parametric equations. a). x=3 (t + 2) 2 ; y = 9t2-5
- Find parametric equations for the tangent line to the curve of intersection of the paraboloid z = x2 + y2 and the ellipsoid 3x2 + 2y2 + 6z2 = 29 at the point (−1, 1, 2).Find the second derivative of y with respect to x from the parametric equations given.x = 3 + 4 sinθ , y = 3cosθ − 4Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = 4 cos(t), y = 4 sin(t), z = 10 cos(2t), (2sqr3, 2, 5,) (x(t), y(t), z(t))= 2 3
- Eliminate the parameter t from the parametric equationsx =3 +sin t and y = cos t - 2.Find the differential equation of the family of ellipses with center at the origin a and the major axis on the y−axis.Find parametric equations for the tangent line at the point(cos(−4π/6),sin(−4π/6),−4π/6) on the curve x=cos(t), y=sin(t), z=(t) x(t)= y(t)= z(t)=