Tangent to a curve intercepts the y-axis at a point `P` A line perpendicular to this tangent through `P` passes through another point `(1,0).` The differential equation of the curve is

Find the equation of a line perpendicular to the line x - 2y + 3 = 0 and passing through the point (1, -2) .

Find the equation of a curve passing through the point (0,0) and whose differential equation is y' = e^(x) sin x .

Find the equation of a curve passing through the point (0,0) and whose differential equation is y'=e^(x)sinx.

Find the equation of the curve passing through the point (1,-1) whose differential equation is xdy=(2x^(2)-1)dx, where xne0 .

The tangent at any point of a circle is perpendicular to the radius through the point of contact.

A curve C has the property that if the tangent drawn at any point P on C meets the co-ordinate axis at A and B , then P is the mid-point of A Bdot The curve passes through the point (1,1). Determine the equation of the curve.

The slope of the tangent at (x , y) to a curve passing through a point (2,1) is (x^2+y^2)/(2x y) , then the equation of the curve is

The perpendicular from the origin to the tangent at any point on a curve is equal to the abscissa of the point of contact. Also curve passes through the point (1,1). Then the length of intercept of the curve on the x-axis is__________

The perpendicular from the origin to the tangent at any point on a curve is equal to the abscissa of the point of contact. Also curve passes through the point (1,1). Then the length of intercept of the curve on the x-axis is__________