# Algebraic proof

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• Feb 22nd 2013, 03:54 PM
Mathshelp246
Algebraic proof
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
• Feb 22nd 2013, 04:09 PM
chiro
Re: Algebraic proof
Hey Mathshelp246.

Hint: First try finding dy/dx through implicit differentiation (this corresponds to your m value).
• Feb 22nd 2013, 05:50 PM
Mathshelp246
Re: Algebraic proof
okay for the problem I got dy/dx to be 2x+10y. dy/dx=0 therefore dy/dx=-2x/10y which simplifies to dy/dx= -x/5y so m= -x/5y (Thinking)
• Feb 22nd 2013, 05:57 PM
Mathshelp246
Re: Algebraic proof
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?
• Feb 22nd 2013, 06:09 PM
chiro
Re: Algebraic proof
Hint: Recall that the equation of the line can take the form y - y0 = m(x - x0) where (x0,y0) is a known point on the line.