Find the equation of the curve whose gradient at `(x,y)` is `y/(2x)` and which passes through the point `(a,2a)`.

Prove that the equation of a curve whose slope at (x,y) is -(x+y)/x and which passes through the point (2,1) is x^2+2xy=8

Find the equation of the circle of radius 5 whose centre lies on y-axis and which passes through the point (3, 2).

Show that the equation of the curve whose slope at any point is equal to y+2x and which passes through the origin is y+2(x+1)=2e^(x)dot

Find the equation of the circle whose centre is (2, -3) and which pass through the point of intersection of 3x+2y=11 and 2x+3y=4 .

Find the equation of the circle whose centre is at the point (4,5) and which passes through the centre of the circle x^2+y^2-6x+4y-12=0.

The equation of the curve whose slope is given by (dy)/(dx)=(2y)/x ; x >0,\ y >0 and which passes through the point (1,1) is

Find the equations of the tangents to the parabola y ^(2) = 6x which pass through the point ((3)/(2), 5).

Find the equation of the circle (i) whose centre is (a,b) which passes through the origin (ii) whose centre is the point (2,3) and which passes through the intersection of the lines 3x-2y-1=0 and 4x+y-27 =0

Find the equation of the tangents to the curve 3x^2-y^2=8 , which passes through the point (4/3,0) .

The equation of the curve satisfying the differential equation y(x+y^3)dx=x(y^3-x)dy and passing through the point (1,1) is