Hint: First try finding dy/dx through implicit differentiation (this corresponds to your m value).
An ellipse has the equation x^2+5y^2=5
a line has the equation y=mx+c
(1) Show that if the line is a tangent to the ellipse then c^2=5m^2+1
(2) hence find the equation of the tangent parallel to the line x-2y+1=0
(note ^ symbol: is the to the power of)
If anyone could help, I would much appreciate it. Thankyou
found c to be : y=mx+c sub in the m value to be y=(-x/5y)x+c therefore y=-x^2/5y+c so, c=y+(x^2/5y) = 5y^2-x^2/5y (putting under a common factor) remembering that 5y^2-x^2=5 in the elipse eq we can sub in for 5?, so therefore the new equation is 5/5y = 1/y?