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Show that the differential equation of all parabolas `y^2 = 4a(x - b)` is given by

A

`y(d^(2)y)/(dx^(2))+(dy)/(dx)=1`

B

`y(d^(2)y)/(dx^(2))+(dy)/(dx)=0`

C

`y(d^(2)y)/(dx^(2))+((dy)/(dx))^(2)=0`

D

`y(d^(2)y)/(dx^(2))+((dy)/(dx))^(2)=1`

Text Solution

Verified by Experts

The correct Answer is:
C
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NIKITA PUBLICATION-Differential Equation-MULTIPLE CHOICE QUESTION
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  2. Fid the differential equation of all the parabolas with latus rectu...

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  3. Show that the differential equation of all parabolas y^2 = 4a(x - b) i...

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  4. The differential equation of all parabolas whose axis are parallel ...

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  5. Form the differential equation of the family of parabolas having ve...

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  6. The differential equation of all parabolas whose axis are parallel ...

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  7. The differential equation (d^(2)y)/(dx^(2))=2 represents which of the ...

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  8. The differential equation for all ellips whose major axis is twice its...

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  9. The equation of the ellips is (x^(2))/(36)+(y^(2))/(16)=k. The differe...

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  10. The differential equation satisfied by sqrt(1-x^(2))+sqrt(1-y^(2))=a(x...

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  11. Consider the equation (x^2)/(a^2+lambda)+(y^2)/(b^2+lambda)=1, where a...

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  12. The differential equation for x^(3)+y^(3)=4ax is

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  13. Form of the differential equation of all family of lines y=mx+(4)/(m) ...

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  14. The differential equation for y^(2)=(x+A)^(3) is

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  15. The differential equation of y = c^(2) + c/x is

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  16. The differential equation, which represents the family of plane curves...

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  17. The differential eqution for (x)/(a)+(y)/(b)=1 is

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  18. From the differential equation by eliminating A and B in Ax^(2)+By^(2...

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  19. The differential equation obtained by eliminating a and b from y = ae^...

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  20. The differential equation of the family of curves y= c(1)e^(x) +c(2)e...

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