What is the differential equation of all parabolas whose Directrices are parallel to the x-axis?

The order of differential equations of all parabolas having directrix parallel to the x-axis is. The equation of all parabolas having directrices parallel to the x-axis is (x – h)2 = ± 4a (y – k).

Which one of the following represents the differential equation of all parabolas having the axes of symmetry coincident with the axis of x?

The differential equation that represents all parabolas having their axis of symmetry coincident with the axis of x, is. yd2ydx2+(dydx)2=0⇒yy2+y21=0.

What is the differential equation of the family of parabolas having their vertices at the origin and their FOCU on the x-axis?

The differential equation of family of parabolas with foci at the origin and axis is y=0. Parabolas having their vertices at the origin and foci on the x-axis.

How do you find equations of parabolas?

The general equation of a parabola is: y = a(x-h)2 + k or x = a(y-k)2 +h, where (h,k) denotes the vertex. The standard equation of a regular parabola is y2 = 4ax.

What is the order and degree of differential equations?

The order of a differential equation is defined to be that of the highest order derivative it contains. The degree of a differential equation is defined as the power to which the highest order derivative is raised.

How do you find the differential equation for a sideways parabola?

The curves are then sideways parabolas with equation y^2 = 4p (x – h). We need to find a differential equation that does not depend on arbitrary constants p and h. Since there are two arbitrary constants to deal with, the differential equation should be second order.

How to use logarithm to solve the family of parabolas?

Since the terms in the equation are positive, one can take logarithm on both sides, First, write the equation for the family of parabolas whose axis is coincident with X axis. Next, we need to eliminate from this equation by differentiation. One can directly differentiate tbe above equation and eliminate to get the solution.

How do you find the location of the focus of a parabola?

Given the equation of a parabola We let (h,0 ) be the location of the vertex, and (h+p,0)be the location of the focus where h will be any number along the x-axis and p is the distance of the focus added to the vertex’s distance h. This is to represent the distance traveled by the focus from the point of origin.

Is a parabola a 2-parameter family of curves?

A parabola with its vertex at (a,0), where ‘a’ can be any real number, and latus rectum as 4b (the factor of 4 is just decorative) has the equation y^2 = 4b (x-a)…. (1). Hence it is a 2-parameter family of curves. Differentiating with respect to x, we get 2y.y’=4b.