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The order and degree of the differential equation of parabolas having vertex at the origin and focus at (a, 0) where a> 0, are respectively
  • a)
    1,1
  • b)
    2,1
  • c)
    1,2
  • d)
    2,2
Correct answer is option 'A'. Can you explain this answer?
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The order and degree of the differential equation of parabolas having ...
The eq. of parabolas having vertex at (0,0) & focus at (a, 0), where (a >0) is:
y2 = 4ax    ...(1)
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The order and degree of the differential equation of parabolas having ...
The order of the differential equation of parabolas having vertex at the origin and focus at (a, 0) is 2.

The degree of the differential equation is 2 as well.

The equation of a parabola with vertex at the origin and focus at (a, 0) can be written as y^2 = 4ax, where a is the distance between the vertex and the focus.

By differentiating both sides of the equation with respect to x, we get:

2yy' = 4a

Simplifying, we have:

yy' = 2a

This is a first-degree differential equation.

To find the second-degree differential equation, we can differentiate both sides of the first-degree equation with respect to x again:

(y')^2 + yy'' = 0

This gives us the second-degree differential equation for the parabola.
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The order and degree of the differential equation of parabolas having vertex at the origin and focus at (a, 0) where a> 0, are respectivelya)1,1b)2,1c)1,2d)2,2Correct answer is option 'A'. Can you explain this answer?
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