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- (a) Where does the normal line to the ellipse x2 -xy + y2 = 3at the point (-1, 1)intersect theellipse a second time?; (b) Illustrate part (a) by graphing the ellipse and the normalline.(a) Where does the normal line to the ellipse x2- x y + y 2 = 3 at the point (1, -1) intersect the ellipse a second time?Let D be the line given by the equation x + 5 = 0. Let E bethe conic section given by the equation x2 + 5y2 = 20. Letthe point C be the vertex of E with the smaller x-coordinate,and let B be the endpoint of the minor axis of E with the largery-coordinate. Determine the exact y-coordinate of the point Mon D that is equidistant from points B and C
- 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 an equation of the normal line to the ellipse x2/32 + y2/8 = 1 at the point (4, 2). (a) Use a graphing utility to graph the ellipse and the normal line. (b) At what other point does the normal line intersect the ellipse?A physicist sends two particles on their way by programming the following parametric equations: Particle A:Pa= (−8 + 3t,12−5t,1 +t) Particle B:Pb= (10−3t,10−2t,−17 + 5t). When the physicist did not see the expected result, they realized that they forgot to change the parameters between particles. Change the parameters, show that the paths do in fact cross but that the particles do not collide.
- A physicist sends two particles on their way by programming the following parametric equations: Particle A: Pa = (−12 + 3t, 43 − 5t, 13 + t) Particle B: Pb = (39 − 3t, 35 − 2t, −36 + 5t) When the physicist did not see the expected result, they realized that they forgot to change the parameters between particles. Change the parameters, show that the paths do in fact cross but that the particles do not collide.6 Select the conic section represented by the equation. 7x 2 + 7y 2 + 3x - 5y - 1 = 0 hyperbola point circle parabola ellipse lineFind an equation of a generating curve given the equation of its surface of revolution. 8x2 + y2 + z2 = 5
- 2 Find the transformed equation of the hyperbola xy = 4 when rotated 45. (x')² - (y')² = 8 (x')²(y')² = 4 (x')² - (y')² = 4A hyperbola in standard position has equation 9x 2 − 15y 2 − 16 = 0. Write down a parametrisation of the part of this hyperbola that lies in the second quadrant (not including any points that lie on the x-axis or y-axis). Make sure that you include any restrictions that are needed on the values of the parameters.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=1