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Chapter 8: Q18P (page 407)

Find the family of orthogonal trajectories of the circles (x-h)2+y2=h2. (See the instructions above Problem 2.31.)

Short Answer

Expert verified

Answer

The family of orthogonal trajectories of the circles:

Step by step solution

01

Given information

The given equation of the circle isx-h2+y2=h2.

02

Standard equation of a circle

The standard equation of a circle is (x-h)2+(y-k)2=r2

Here, (h,k)is the center of the circle and r is the radius of the circle.

03

The orthogonal trajectories of the circle

The given equation of the circle is,

x-h2+y2=h2

The standard equation of a circle is

x-h2+y-k2=r2............i

where h,k is the center of the circle and r is the radius of the circle.

Now, compare equation (1) with the standard form of equation, which indicates that

h,0is the center of the circle and h is the radius of the circle.

Therefore, it can be said that the equation (1) shows a family of circles with center h,0and radius h. The value of h varies from 鈭�to 鈭�.

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