In how many points the line `y+14=0` cuts the curve whose equation is `-x(x^2+x+1)=0?`

Find the lines whose combined equation is 6x^2+5x y-4y^2+7x+13 y-3=0

Find the equation of the curve passing through the point (1,1) whose differential equation is x dy = (2x^(2) + 1) dx(x ne 0) .

Find the equation of the normals to the circle x^2+y^2-8x-2y+12=0 at the point whose ordinate is -1

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 straight line joining the points of intersection of the lines 3x+2y+1=0 and x+y=3 to the intersection of the lines y-x=1 and 2x+y+2=0

Find the combined equation of the straight lines whose separate equations are x-2y-3=0 and x+y+5=0.

Find the combined equation of the straight lines whose separate equations are x-2y-3=0 and x+y+5=0