Maths-
General
Easy

Question

The differential equation of all conics with the coordinate axes, is of order

  1. 1
  2. 2
  3. 3
  4. 4

Hint:

In this question we have to find the order of the differential equation of all conics with the coordinate axis. First we will find the differential equation by differentiating the equation twice then we will get the order.

The correct answer is: 2


    e q u a t i o n space space x squared over a squared plus y squared over b squared equals 1
d i f f e r e n t i a t i n g space w. r. t space x comma
fraction numerator d over denominator d x end fraction x squared over a squared plus fraction numerator d over denominator d x end fraction y squared over b squared equals fraction numerator d over denominator d x end fraction 1
rightwards double arrow fraction numerator 2 x over denominator a squared end fraction plus fraction numerator 2 y. y apostrophe over denominator b squared end fraction equals 0
rightwards double arrow fraction numerator 2 y. y apostrophe over denominator b squared end fraction equals fraction numerator negative 2 x over denominator a squared end fraction
rightwards double arrow fraction numerator y. y apostrophe over denominator b squared end fraction equals fraction numerator negative x over denominator a squared end fraction
rightwards double arrow fraction numerator y. y apostrophe over denominator x end fraction equals fraction numerator negative b squared over denominator a squared end fraction........ e q u space 1
a g a i n space d i f f e r e n t i a t i n g space
fraction numerator d over denominator d x end fraction x over a squared plus fraction numerator d over denominator d x end fraction fraction numerator y. y apostrophe over denominator b squared end fraction equals 0
1 over a squared plus 1 over b squared open parentheses y apostrophe. y apostrophe plus y. y apostrophe apostrophe close parentheses equals 0
open parentheses y apostrophe close parentheses squared plus y. open parentheses y apostrophe apostrophe close parentheses equals fraction numerator negative b squared over denominator a squared end fraction..... space e q u space 2
f r o m space 1 space a n d space 2
y over x. y apostrophe equals open parentheses y apostrophe close parentheses squared plus y. open parentheses y apostrophe apostrophe close parentheses
rightwards double arrow y. y apostrophe equals x. open parentheses y apostrophe close parentheses squared plus x. y. open parentheses y apostrophe apostrophe close parentheses
S o comma space t h e space o r d e r space i s space 2.

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