ATAR Notes: Forum
VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: PolySquared on February 22, 2018, 12:54:07 pm
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Can I get some help on how to solve this?
Find the equation of the straight line(s) which pass through the point (1, −2) and is (are) tangent to the parabola with equation y = x^2.
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What progress have you made so far?
I'll try get you started: The equation of a line can be written in the form y = mx + c. Since we know that this line passes through (1, -2), we can sub this point in, giving c = -m-2. We can therefore rewrite the equation of our line as y = mx - m - 2. Since the question asks us to find the equation of the line, our end goal is to find suitable values for m, and substitute these into the equation for our line. We know that the line and parabola intersect (once, as a tangent), so we can solve mx - m - 2 = x2. Note that since the line is tangent to the parabola, we are looking for one solution. Where can we go from here, to eventually give us the equation of the line? (Hint: Discriminant)
Hope this helps :)