A normal at any point `(x , y)` to the curve `y=f(x)` cuts a triangle of unit area with the axis, the differential equation of the curve is

The differential equation of the curve x/(c-1)+y/(c+1)=1 is

The normal at the point (1,1) on the curve 2y + x^(2) = 3 is

lf length of tangent at any point on th curve y=f(x) intercepted between the point and the x-axis is of length 1. Find the equation of the curve.

A normal is drawn at a point P(x , y) of a curve. It meets the x-axis at Qdot If P Q has constant length k , then show that the differential equation describing such curves is y(dy)/(dx)=+-sqrt(k^2-y^2) . Find the equation of such a curve passing through (0, k)dot

The normal lines to a given curve at each point (x,y) on the curve pass through the point (2,0) the curve passes through the point (2,3) formulate the differential equation representign the problem and hecne find the equation of the curve

The gradient (siope) of a curve at any point (x,y) is (x^(2)-4)/(x^(2)) . If the curve passes through the point (2 , 7) , then the equation of the curve is ,

The slope at any point of the curve y = f(x) is given by (dy)/(dx)= 2x it passes through (1,-1) then the equation of the curve is :

A curve y=f(x) passes through point P(1,1) . The normal to the curve at P is a (y-1)+(x-1)=0 . If the slope of the tangent at any point on the curve is proportional to the ordinate of the point, then the equation of the curve is

The gradient (slope) of a curve at any point (x,y) is (x^(2) -4)/(x^(2)) . If the curve passes through the point (2,7) , then the equation of the curve is. . . .