The path travelled by a long period comet as it passes near the sun is described by a hyperbola. Observations through the Keck Observatory in Hawaii indicates that the equation representing the path of the comet could be derived from the homogeneous first order ordinary differential equation (x – 3y)dx - 3 (x – 3y)dy = 0 where x and y are the spatial coordinates of the location of the comet along the plane of its motion. On this plane lies also the sun, which is located at an arbitrary point called the origin. At a particular point in time, the Keck telescope observed that, on this designated coordinate plane, the coordinates of the comet is at x = -1 light year (negative indicates that the comet is at the left of the sun on this plane) and y = 1 light year. Find the unique curve which represents the motion of the comet at the indicated instant.
The path travelled by a long period comet as it passes near the sun is described by a hyperbola. Observations through the Keck Observatory in Hawaii indicates that the equation representing the path of the comet could be derived from the homogeneous first order ordinary differential equation (x – 3y)dx - 3 (x – 3y)dy = 0 where x and y are the spatial coordinates of the location of the comet along the plane of its motion. On this plane lies also the sun, which is located at an arbitrary point called the origin. At a particular point in time, the Keck telescope observed that, on this designated coordinate plane, the coordinates of the comet is at x = -1 light year (negative indicates that the comet is at the left of the sun on this plane) and y = 1 light year. Find the unique curve which represents the motion of the comet at the indicated instant.
The path travelled by a long period comet as it passes near the sun is described by a hyperbola. Observations through the Keck Observatory in Hawaii indicates that the equation representing the path of the comet could be derived from the homogeneous first order ordinary differential equation (x – 3y)dx - 3 (x – 3y)dy = 0 where x and y are the spatial coordinates of the location of the comet along the plane of its motion. On this plane lies also the sun, which is located at an arbitrary point called the origin. At a particular point in time, the Keck telescope observed that, on this designated coordinate plane, the coordinates of the comet is at x = -1 light year (negative indicates that the comet is at the left of the sun on this plane) and y = 1 light year. Find the unique curve which represents the motion of the comet at the indicated instant.
Transcribed Image Text:The path travelled by a long period comet as it passes near the sun is described by a hyperbola.
Observations through the Keck Observatory in Hawaii indicates that the equation representing the path of
the comet could be derived from the homogeneous first order ordinary differential equation (x – 3y)dx –
3(x – 3y)dy = 0 where x and y are the spatial coordinates of the location of the comet along the plane of
its motion. On this plane lies also the sun, which is located at an arbitrary point called the origin. At a
particular point in time, the Keck telescope observed that, on this designated coordinate plane, the
coordinates of the comet is at x = -1 light year (negative indicates that the comet is at the left of the sun
on this plane) and y = 1 light year. Find the unique curve which represents the motion of the comet at the
indicated instant.
With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.
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