A tangent and a normal to a curve at any point P meet the x and y axes at A, B and C, D respectively. Find the equation of the curve passing through `(1, 0)` if the centre of circle through `O.C, P and B` lies on the line y = x (where O is the origin).

Find the equation of a curve passing through (1,1) and whose slope of tangent at a point (x, y) is -(x)/(y) .

Find the equation of the curve passing through the point (1,0) if the slope of the tangent to the curve at any point (x ,y)i s(y-1)/(x^2+x)dot

If slope of the tangent at the point (x, y) on the curve is (y-1)/(x^(2)+x) , then the equation of the curve passing through M(1, 0) is :

The ordinate and the normal at any point P on the curve meet the x-axis at points A and B respectively. Find the equation of the family of curves satisfying the condition , The product of abscissa of P and AB =arithmetic mean of the square of abscissa and ordinate of P .

Find the equation of the curve passing through the point, (5,4) if the sum of reciprocal of the intercepts of the normal drawn at any point P(x,y) on it is 1.

The equation of the circle which passes through the point A(0, 5) and B(6, 1) and whose centre lies on the line 12x+5y=25 is

The equation of the circle which passes through the point A(0, 5) and B(6, 1) and whose centre lies on the line 12x+5y=25 is

Find the equation of the circle passing through the origin and the points where the line 3x+4y=12 meets the axes of coordinates.

Find the equation of the line which passes through P(1,-7) and meets the axes at A and B respectively so that 4A P-3B P=0.

Find the equation of the curve through the point (1,0), if the slope of the tangent to the curve at any point (x,y) is (y-1)/(x^(2)+x)