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- The ellipse x^2/7^2 + y^2/6^2 = 1can be drawn with parametric equations where x(t) is written in the formx(t)=rcos(t) with r = and y(t)The ellipse ((x^2)/(3^2))+((y^2)/(8^2))=1 can be drawn with parametric equations where x(t) is written in the form x(t)=rcos(t) with r= and y(t)=The ellipse x^2/2^2+y^2/7^2=1 can be drawn with parametric equations where x(t) is written in the form x(t)=r cos(t) r= ? and y(t)= ?
- Find the differential equation of the family of ellipses with center at the origin a and the major axis on the y−axis.Consider a particle traveling clockwise on the elliptical path x2/ 100 + y2/25 = 1. The particle leaves the orbit at the point (−8, 3) and travels in a straight line tangent to the ellipse. At what point will the particle cross the y-axis?Find a parametric description for the ellipse 9x^2+4y^2+24y=0, oriented clockwise and where t=0 corresponds to (0, 0)
- Find parametric equations for an object moving clockwise along the ellipse (x2/16)+(y2/9)=1 beginning at (4,0) and requiring 2 seconds for a complete revolution.A lizard moves through the plane with its position at t seconds given by the parametric equations x=3cos(2pi t)+2, y= -6cos(2pi t)+1. The lizard begins moving at t=0 seconds. a. How long does it take for the lizard to return to its starting position for the first time? b. how far does it go in 4 seconds?Find a parametric equation for the path of a particle that moves halfway around the circle (x^2)+(y-1)^2 = 9 counterclockwise, if the particle starts at (0,4). Let x and y be in terms of t for t between 0 and pi.
- If I have a pair of parametric equations x=20cos(t) and y=10sin(t) How can I increase the speed of the particle moving in these path x2/400 + y2/100=1On the ellipse x^2 + 9y^2 = 9, find d2^y/dx^2 using implicit differentiation. Your final answer may involve both x and yFind the point on the ellipsoid x2 + y2/4 + z2/9 = 1 for which x + y + z is largest.