NCERT Class 12-Mathematics: Chapter –9 Differential Equations Part 11

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Question 31:

Find the equation of a curve passing through origin if the slope of the tangent to the curve at any point is equal to the square of the difference of the abscissa and ordinate of the point.

Answer:

Slope of tangent to the curve and difference of abscissa and ordinate

According to the question,

Put

On substituting these values in Eq. (i), we get

On integrating both sides, we get

Since, the curve passes through the origin.

On substituting the value of C in Eq. (ii), we get

Question 32:

Find the equation of a curve passing through the point . If the tangent drawn at any point on the curve meets the co-ordinate axes at A and B such that P is the mid-point of AB.

Answer:

The below figure obtained by the given information

Find the equation of a curve

Find the Equation of a Curve

Loading image

Let the coordinate of the point is It is given that, P is mid-point of AB.

So, the coordinates of points A and B are respectively.

Since, the segment AB is a tangent to the curve at P.

On integrating both sides, we get

Since, the given curve passes through