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Find the equation of a curve passing through the point (1, 1). If the tangent drawn at any point P (x, y) on the curve meets the co-ordinate axes at A and B such that P is the mid-point of AB.
Find the equation of a curve passing through the point (1, 1). If the tangent drawn at any point P (x, y) on the curve meets the co-ordinate axes at A and B such that P is the mid-point of AB.
CBSE | Class 12 | Differential Equations | Exercise 1 | Maths | NCERT Exemplar
Find the equation of a curve passing through the point (1, 1). If the tangent drawn at any point P (x, y) on the curve meets the co-ordinate axes at A and B such that P is the mid-point of AB.

Let \[P\left( x\text{ },\text{ }y \right)\] be any point on the curve,

AB be the tangent to the given curve at P.

A/Q, P is the mid-point of AB

HENCE,

the coordinates of \[A\text{ }is\text{ }\left( 2x,\text{ }0 \right)\text{ }and\text{ }B\text{ }is\text{ }\left( 0,\text{ }2y \right).\]

NCERT Exemplar Solutions Class 12 Mathematics Chapter 9 - 58

Also,

The slope of the tangent AB

\[=\text{ }\left( 2y\text{ }\text{ }0 \right)/\text{ }\left( 0\text{ }\text{ }2x \right)\text{ }=\text{ }-y/x\]

NCERT Exemplar Solutions Class 12 Mathematics Chapter 9 - 59

And hence, required equation is \[xy\text{ }=\text{ }1\]

 

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