Advertisements
Advertisements
Question
Form the differential equation of the family of circles having centre on y-axis and radius 3 units.
Solution
Let the centre of the circle on y-axis be (0, b).
The differential equation of the family of circles with centre at (0, b) and radius 3 is as follows:
`x^2+(y - b)^2 = 3^2`
Differentiating equation (1) with respect to x, we get:
This is the required differential equation.
APPEARS IN
RELATED QUESTIONS
Form the differential equation of the family of circles touching the y-axis at the origin.
Form the differential equation of the family of ellipses having foci on y-axis and centre at origin.
Form the differential equation of the family of hyperbolas having foci on x-axis and centre at origin.
For the curve y = 5x – 2x3, if x increases at the rate of 2 units/sec, then find the rate of change of the slope of the curve when x = 3
Show that the family of curves for which `dy/dx = (x^2+y^2)/(2x^2)` is given by x2 - y2 = cx
Form the differential equation from the following primitive where constants are arbitrary:
y = cx + 2c2 + c3
Form the differential equation corresponding to y2 − 2ay + x2 = a2 by eliminating a.
Form the differential equation corresponding to (x − a)2 + (y − b)2 = r2 by eliminating a and b.
Form the differential equation of the family of curves represented by the equation (a being the parameter):
(2x − a)2 − y2 = a2
Form the differential equation of the family of curves represented by the equation (a being the parameter):
(x − a)2 + 2y2 = a2
Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
x2 + y2 = a2
Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
y2 = 4ax
Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
y2 = 4a (x − b)
Show that y = bex + ce2x is a solution of the differential equation, \[\frac{d^2 y}{d x^2} - 3\frac{dy}{dx} + 2y = 0\]
Find one-parameter families of solution curves of the following differential equation:-
\[\frac{dy}{dx} - \frac{2xy}{1 + x^2} = x^2 + 2\]
Find one-parameter families of solution curves of the following differential equation:-
\[\frac{dy}{dx} + y \cos x = e^{\sin x} \cos x\]
Find one-parameter families of solution curves of the following differential equation:-
\[\left( x + y \right)\frac{dy}{dx} = 1\]
Find one-parameter families of solution curves of the following differential equation:-
\[\frac{dy}{dx} \cos^2 x = \tan x - y\]
Find one-parameter families of solution curves of the following differential equation:-
\[e^{- y} \sec^2 y dy = dx + x dy\]
Find one-parameter families of solution curves of the following differential equation:-
\[x \log x\frac{dy}{dx} + y = 2 \log x\]
Find one-parameter families of solution curves of the following differential equation:-
\[x\frac{dy}{dx} + 2y = x^2 \log x\]
Write the differential equation representing family of curves y = mx, where m is arbitrary constant.
The differential equation which represents the family of curves y = eCx is
The family of curves in which the sub tangent at any point of a curve is double the abscissae, is given by
Form the differential equation representing the family of curves `y2 = m(a2 - x2) by eliminating the arbitrary constants 'm' and 'a'.
Find the area of the region bounded by the curves (x -1)2 + y2 = 1 and x2 + y2 = 1, using integration.
Form the differential equation representing the family of curves y = A sin x, by eliminating the arbitrary constant A.
The differential equation representing the family of curves y = A sinx + B cosx is ______.
Form the differential equation by eliminating A and B in Ax2 + By2 = 1
Find the equation of a curve passing through (2, 1) if the slope of the tangent to the curve at any point (x, y) is `(x^2 + y^2)/(2xy)`.
Find the equation of a curve passing through origin if the slope of the tangent to the curve at any point (x, y) is equal to the square of the difference of the abcissa and ordinate of the point.
The differential equation of the family of curves x2 + y2 – 2ay = 0, where a is arbitrary constant, is ______.
The differential equation of the family of curves y2 = 4a(x + a) is ______.
The differential equation representing the family of circles x2 + (y – a)2 = a2 will be of order two.
From the differential equation of the family of circles touching the y-axis at origin
