Home » Applications » Page 2

# Find a Cartesian equation for the pursuit path for given parameters

Let Q be a point which moves upward along the positive y-axis and let P be a point which starts at (1,0) and pursues Q according to an equation which stipulates that the distance from P to the y-axis is exactly \frac{1}{k} times the distance from Q to the origin for a positive number. Find the Cartesian equation for the path of pursuit the point P traces out.

Incomplete.

# Find a Cartesian equation for the pursuit path of given parameters

Let be a point which moves upward along the positive -axis and let be a point which starts at and pursues according to an equation which stipulates that the distance from to the -axis is exactly the distance from to the origin. Find the Cartesian equation for the path of pursuit the point traces out.

Incomplete.

# Find the orthogonal trajectories of the family of all circles passing through (1,1) and (-1,-1)

Find the orthogonal trajectories of the family of curves consisting of all circles passing through the points and .

In a previous exercise (section 8.22, Exercise #12) we found that the family of all circles passing through the points and satisfy the differential equation

Therefore, the orthogonal trajectories satisfy the differential equation

Incomplete.

# Find the orthogonal trajectories of the family of all circles passing through the points (1,0) and (-1,0)

Find the orthogonal trajectories of the family of curves consisting of all circles passing through the points and .

In a previous exercise (section 8.22, Exercise #11) we found that the family of all circles passing through the points and satisfy the differential equation

Therefore, the orthogonal trajectories satisfy the differential equation

Incomplete.

# Find the orthogonal trajectories of the family y = C cos x

Find the orthogonal trajectories of the family of curves given by

First, we find that the family of curves satisfies the differential equation

Since we then have

Therefore, the orthogonal trajectories satisfy the differential equation

# Find the orthogonal trajectories of the family x2 – y2 = C

Find the orthogonal trajectories of the family of curves given by

First, we find that the family of curves satisfies the differential equation

Therefore, the orthogonal trajectories satisfy the differential equation

# Find the orthogonal trajectories for the family y = Ce-2x

Find the orthogonal trajectories of the family of curves given by

First, this family of curves satisfies the differential equation

Since we then have

Hence, the orthogonal trajectories satisfy the differential equation

# Find the orthogonal trajectories of the family x2y = C

Find the orthogonal trajectories of the family of curves given by

From the family of curves, we find that all of the curves in the family satisfy the differential equation

Therefore, the orthogonal trajectories satisfy the differential equation

Hence we have

# Find the orthogonal trajectories of the family y2 = Cx

Find the orthogonal trajectories of the family of curves by

From the family of curves, we find a differential equation the curves all satisfy,

Since we then have,

Therefore, the orthogonal trajectories satisfy the differential equation

# Find the orthogonal trajectories of the family x2 + y2 + 2Cy = 1

Find the orthogonal trajectories of the family of curves given by

Incomplete.