What is the differential equation for the family of circles with Centres on the x-axis?

The equation of a circle with centre at (h, k) and radius equal to a, is (x – h)2 + (y – k)2 = a2. When the circle passes through the origin and centre lies on x-axis i.e., h = a and k = 0.

What is the differential equation of the family of circles with center on the origin?

xdx+ydy=0.

Which of the following is the equation of family of unit circle tangent to x-axis?

The formula for the equation of a circle is (x – h)2+ (y – k)2 = r2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle. If a circle is tangent to the x-axis at (3,0), this means it touches the x-axis at that point.

How do you solve the curved family?

Starts here41:09Differential Equations – Families of Curves Solved Problems – YouTubeYouTubeStart of suggested clipEnd of suggested clip60 second suggested clipThis will now be the family of curves. The of parabolas having their vertices of the origin theMoreThis will now be the family of curves. The of parabolas having their vertices of the origin the force I on the y-axis or in other words if you have only one degree 4 the dy over DX. So we can rewrite.

How do you find the equation of the family of a circle?

The equation of the family of circles touches the line y – y1 = m (x – x1) at (x1, y1) for any values of m is (x – x1)2 + (y – y1)2 + λ[(y – y1) – m(x – x1)] = 0. Here, we can have two sub-cases according as whether the line is parallel to x -axis or y-axis.

What is the differential equation of the family of parabola?

xy′+2y+2=0.

How do you find the differential equation of a circle?

⇒c=0. We get the equation of the circle as x2+y2+2px+2qy=0. Now, let us substitute y=0 in the circle x2+y2+2px+2qy=0 as the circle touches x-axis. So, we get x2+(0)2+2px+2q(0)=0.

What is Families of curves differential equation?

A set of curves whose equations are of the same form but which have different values assigned to one or more parameters in the equations. Families of curves arise, for example, in the solutions to differential equations with a free parameter (Harris and Stocker 1998, p. 649).

How is a differential equation derived from the equation representing family of curves?

The family of curves whose differential equation has to be obtained is represented by $v = \dfrac{A}{r} + B$ is given where A and B are arbitrary constants.

What is the family of circles of radius r and tangent?

Equation of family of circles of radius r and tangent to the y-axis: (x ± r) 2 + (y – k) 2 = r 2 The (±) sign indicates that circles can be at the left or at the right of y-axis. There is only one arbitrary constant k, thus, the differential equation is a first degree.

What is the equation of system of circles touching y axis at origin?

Equation of a circle with centre at (a,0) and radius a. (x─a)²+(y─0)² = a². That is, x²+y²─2ax = 0 ─────► (1) The above equation represents the family of circles touching Y axis at origin. Here ‘a’ is an arbitrary constant. In order to find the differential equation of system of circles touching Y axis at origin,

What is the centre of a circle with radius x?

For any such circle the centre must be at a distance equal to its radius, from the x-axis. where r may be any fixed real number, not necessarily positive and c is an arbitrary constant. Differentiating with respect to x, we get

What does the (±) sign mean in the differential equation?

The (±) sign indicates that circles can be at the left or at the right of y-axis. There is only one arbitrary constant k, thus, the differential equation is a first degree.