Prove that the curve represented by `x=3(cost+sint),y=4(cost-sint),t in R ,` is an ellipse

Find the equation of tangent and normal to the curve given by x=7cost andy=2sint,tinR at any point on the curve.

Find the equation of tangent and normal to the curve given by x = 7 cos t and y = 2 sin t, t in R at any point on the curve.

Find (dy)/(dx) if x =a (t-sint),y=a(1-cos t)?

Distance between the foci of the curve represented by the equation x=3+4cosθ,y=2+3sinθ is

The curve represented by the equation sqrt(p x)+sqrt(q y)=1 where p ,q in R ,p ,q >0, is a circle (b) a parabola an ellipse (d) a hyperbola

Find the derivatives of the following : x=a(cost+tsint), y=a(sint-tcost)

A ripple tank demostrates the effect of two water being added together. The two waves are described by h=8 cost and h=6 sint , where t in [0,2pi) is in second and h is the height in millimeters above still water. Find the maximum height of the resultant wave and the value of t at which it occurs.

The equation of the normal to the curve parametrically represented by x=t^(2)+3t-8 and y=2t^(2)-2t-5 at the point P(2,-1) is

Locus of centroid of the triangle whose vertices are (a cost, a sint), (b sint,b cost) and (1, 0), where t is a parameter, is