# urgent parabola problem plz help!

• Jan 2nd 2009, 08:06 AM
mohamedsafy
urgent parabola problem plz help!
prove that the line x+y=1 touches the parabola y=x-x^2 and determine the do ordinates of point of tangency
• Jan 2nd 2009, 08:14 AM
Isomorphism
Quote:

Originally Posted by mohamedsafy
prove that the line x+y=1 touches the parabola y=x-x^2 and determine the do ordinates of point of tangency

If P(a,b) is the point of tangency, then P lies on both x+y = 1 and y = x - x^2. So a+b = 1 and b = a - a^2.

Thus $b = 1 - a = a - a^2 \implies a^2 - 2a + 1 = 0 \implies a = 1$. Thus b = 1 - a = 0.

Thus P(1,0) is the point of tangency.