Home
Class 12
MATHS
Find the equation of all possible curves...

Find the equation of all possible curves such that length of intercept made by any tangent on X-axis is equal to the square of X-coordinate of the point of tangency. Given that the curve passes through (2,1) .

Text Solution

Verified by Experts

The correct Answer is:
Possible curve are `y=(x)/(2(x-1)) or y=(3x)/(2(1+x))`
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the curve for which the intercept cut off by any tangent on y-axis is proportional to the square of the ordinate of the point of tangency.

The x-intercept of the tangent to a curve is equal to the ordinate of the point of contact. The equation of the curve through the point (1,1) is

A curve passing through (1, 0) is such that the ratio of the square of the intercept cut by any tangent on the y-axis to the Sub-normal is equal to the ratio of the product of the Coordinates of the point of tangency to the product of square of the slope of the tangent and the subtangent at the same point, is given by

The Curve possessing the property text the intercept made by the tangent at any point of the curve on the y-axis is equal to square of the abscissa of the point of tangency, is given by

Find the equation of a curve passing through the origin given that the slope of the tangent to the curve at any point (x, y) is equal to the sum of the coordinates of the point.

Find the points on the curve y=x^(3) at which the slope of the tangent is equal to the y - coordinate of the point.

The curve for which the ratio of the length of the segment intercepted by any tangent on the Y-axis to the length of the radius vector is constant (k), is

Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point (2, 3) .