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If the line x+y=a touches the parabola y...

If the line `x+y=a` touches the parabola `y=x-x^2,` then find the value of `a`.

Text Solution

Verified by Experts

The correct Answer is:
a=1
Eliminating y, we have
`a-x=x-x^(2)orx^(2)-2x+a=0`
Since the touches the parabola, we must have equal roots.
Therefore,
4-4a=0 or a=1
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