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