JEE MAIN - Mathematics (2003 - No. 23)
The degree and order of the differential equation of the family of all parabolas whose axis is $$x$$-axis, are respectively.
$$2, 3$$
$$2,1$$
$$1,2$$
$$3,2.$$
Explanation
General equation of parabola whose axis is along X-axis
$${y^2} = 4a\left( {x - h} \right)$$
Differentiating with respect to x, we get
$$2y{y_1} = 4a$$
$$ \Rightarrow y{y_1} = 2a$$
Again differentiating with respect to x, we get
$$ \Rightarrow {y_1}^2 + y{y_2} = 0$$
Degree $$=1,$$ order $$=2.$$
$${y^2} = 4a\left( {x - h} \right)$$
Differentiating with respect to x, we get
$$2y{y_1} = 4a$$
$$ \Rightarrow y{y_1} = 2a$$
Again differentiating with respect to x, we get
$$ \Rightarrow {y_1}^2 + y{y_2} = 0$$
Degree $$=1,$$ order $$=2.$$
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