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Problem 63 Medium Difficulty

Draw a diagram to shoe that there are two tangent lines to the parabola $ y = x^2 $ that pass through the point (0, -4). Find the coordinates of the point where these tangent lines intersect the parabola.

Answer

$\left(a, a^{2}\right)$ also lies on the line, $a^{2}=2 a(a)-4,$ or $a^{2}=4 .$ So $a=\pm 2$ and the points are (2,4)
and (-2,4)

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Video Transcript

Hey, it's Claire. So when you read here So we're gonna note that all points of the problem Why equals X square or the form ex calmer X square in the 10 gin A comma a square pass History zero common negative floor We know that the slope of attention at any point is the derivative. So when we do a friend a tree we have two x So the slough off the tension at a comma A square iss to a And since this tension passes street of slope Hey, do the 0.8 common Any square and zero common negative four. We can write the slip detention as a square plus four over a which is equal to to a and then we get a is equal to positive or negative too. One of the tensions is to come before and the other is negative to Palmer for when we draw a graph, it looks like this men are tensions are gonna be in blue. This is Siro common negative for to karma four negative too common for