prove that the line x+y=1 touches the parabola y=x-x^2 and determine the do ordinates of point of tangency
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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 $\displaystyle b = 1 - a = a - a^2 \implies a^2 - 2a + 1 = 0 \implies a = 1$. Thus b = 1 - a = 0. Thus P(1,0) is the point of tangency.
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