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The differential equation of all conics ...

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

A

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

B

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

C

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

D

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

Text Solution

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The correct Answer is:
C
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Correct statement is/are (A) The differential equation of all conics whose axes coincide with the axes of co-ordinates is of order 2 (B) The differential equation of all staright lines which are at fixed distance p from origin is of degree 2. (C) The differential equation of all parabola each which has a latus rectum 4a & whose axes are parallel to y-axis is of order 2. D) The differential equation of all parabolas of given vertex, is of order 3.

What is the order of the differential equation of all ellipses whose axes are along the coordinate axes?

Knowledge Check

  • The differential equation of all ellipse centered at the origin axis being coordinate axes is:

    A
    `xy y_2 - xy _(1) ^(2) + y y_1=0`
    B
    ` y _2 + xy_(1) ^(2) - y y _1=0`
    C
    `xy y_2 + xy_1^2 + y y _1 =0`
    D
    none of these

  • The differential equation of all circles in the first quadrant which touch the coordiante axes is of order

    A
    1
    B
    2
    C
    3
    D
    none of these

  • Statement I The order of differential equation of all conics whose centre lies at origin is , 2. Statement II The order of differential equation is same as number of arbitary unknowns in the given curve.

    A
    Statement I is true ,and Statement II is the correct explanation for Statement I.
    B
    Statement I is true, Statement II is true and Statement II is the correct explanation for Statment I
    C
    Statement I is true, Statement II is false.
    D
    Statement I is false, Statement II is true.

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    The differential equation of all conics whose centre lie at the origin is of order

    What is the degree of the differential equation of all circles touching both the coordinate axes in the first quadrant?

    Regular coordinate axes

    An ellipse passes through the point (4,-1) and touches the line x+4y-10=0. Find its equation if its axes coincide with the coordinate axes.

    Find the differential equation of all the circles in the first quadrant which touch the coordinate axes.

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