Find parametric equations and a parameter interval for the motion of a particle starting at the point (5, 0) and tracing the top half of the circle x2+y2 = 25 ten times. Find parametric equations for the particle's motion. Let the parameter interval for the motion of the particle be 0 ≤ t ≤ 10π. x = y = (Type expressions using t as the variable. )
Find a parameterization for the circle (x−14)2 + y2 = 49 starting at the point (7, 0) and moving clockwise once around the circle. Find parametric equations for the circle. x = , y = , 0 ≤ θ ≤ 2π
Find the point(s) on the ellipse x = 2 cost, y = sint, 0 ≤ t ≤ 2π closest to the point (324, 0). (Hint: Minimize the square of the distance as a function of t. ) The point(s) on the ellipse closest to the given point is(are) (Type ordered pairs. Use a comma to separate answers as needed. )
Find an equation for the line tangent to the curve at the point defined by the given value of t. Also, find the value of d2y dx2 at this point. x = 4 sint, y = 2 cost, t = π4 The equation represents the line tangent to the curve at t = π4. (Type an exact answer, using radicals as needed. ) The value of d2y dx2 at t = π4 is (Type an exact answer, using radicals as needed. )
Find an equation for the line tangent to the curve at the point defined by the given value of t. Also, find the value of d2y dx2 at this point. x = sec2t−1, y = cost; t = −π3 Write the equation of the tangent line. (Type exact answers, using radicals as needed. ) What is the value of d2y dx2 at this point? d2y dx2 = (Type an exact answer, using radicals as needed. )
Find an equation for the line tangent to the curve at the point defined by the given value of t. Also, find the value of d2y dx2 at this point. x = 2t3 + 4, y = t6, t = −1 Write the equation of the tangent line. y = What is the value of d2y dx2 at this point? d2y dx2 = (Type an integer or a simplified fraction. )