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- Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle rolls along the x -axis given that P is at a maximum when x=0.Obtain the dirfferential equation of the family of curves: 1. All circles passing through the origin and (0,4)sorry I forget can you find for me all points where G is preserving orientation? Sorry, I forgot it.
- Through any point (x, y) of a certain curve which passes through the origin. lines are dawn parallel To the coordinate axes. Find the curve given that it divides the rectangle fomed by the two lines and the axes into two areas, one of which is three times the other.Show that the path given by r(t) = (cos t,cos(2t), sint) intersects the xy-plane infinitely many times, but the underlying space curve intersects the xy-plane only twice.A circle with center at the origin and radius equal to a meets the axis of x at A and B.P(alpha) and Q(beta) are two points on the circle so that alpha-beta=2gamma,where gammais a constant.Find the locus of the point of intersection of AP and BQ.
- Suppose that a projectile is fired into a headwind that pushes it back so as to reduce its horizontal speed by a constant amount. Find parametric equa- tions for the path of the projectile.A circle with center at the origin and radius equal to a meets the axis of x at A and B.P(alpha) and Q(beta) are two points on the circle so that alpha-beta=2gamma,where gamma is a constant.Find the locus of the point of intersection of AP and BQ.Let P, Q be two points on the sphere of radius 1. Assume that P ≠ -Q. Show that there exists a curve joining P and Q on the sphere of radius 1, centered at the origin.