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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 differential equation of the family of plane curves described. 1. All ellipses having its centers at the origin and traverse axis x.A cable hangs between two poles of equal height and 24 feet apart. Set up a coordinate system where the poles are placed at x=−12 and x=12, where x is measured in feet. The height (in feet) of the cable at position x is h(x)=18cosh(x/18), where cosh(x)=(ex+e−x)/2 is the hyperbolic cosine
- Obtain the differential equation of the plane curves described. 2. Family of ellipses with center at the origin.Two circles of radius 4 are tangent to the graph of y2=4x at the point (1,2). Find equations of these two circles. (Enter your answers as a comma separated list)Find parametric equations for line that is tangent to the curve x=cost, y=sint, z=t at the point(cos(4π/6),sin(4π/6),4π/6) Parametrize the line so that it passes through the given point at t=0.
- Find parametric equations for the tangent line to the curve with the parametric equationsx =sqrt(t^2 + 3), y = ln(t^2 + 3), z = tat the point (2, ln4, 1). show all steps1. Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x= e−2t cos(2t), y = e−2t sin(2t), z = e−2t; (1, 0, 1) 2. Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = e−2t cos(2t), y = e−2t sin(2t), z = e−2t; (1, 0, 1) 3. Reparametrize the curve with respect to arc length measured from the point where t = 0 in the direction of increasing t. (Enter your answer in terms of s.) r(t) = 4t i + (5 − 2t) j + (1 + 3t) kHow would this parametric function of x=2cost +cos2t; y=2sint-sin2t be solved
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