SOLUTION: Find the points on y=x^2+5 where a line drawn from the origin can touch the curve. Thanks

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Question 827548: Find the points on y=x^2+5 where a line drawn from the origin can touch the curve.
Thanks
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Between x=-sqrt%285%29 and x=sqrt%285%29

Derivative of y=x^2+5 gives the formula for slope of any point on the parabola.
Slope formula or derivative for this is y'=2x, again, representing a slope of a line.

The line containing the origin and using that slope of 2x, would be y=%282x%29x%2B0 or simply y=2x%5E2.

Two lines must intersect: The parabola, and that tangent line.
What is the x value for the intersection of these two equations?
y=x%5E2%2B5 with y=2x%5E2...
'
x%5E2%2B5=y=2x%5E2
5=x%5E2
x=-sqrt%285%29 or x=sqrt%285%29

The domain for this ability to touch the parabola from the orginin in without missing the parabola is highlight%28-sqrt%285%29%3C=x%3C=sqrt%285%29%29