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Math challengeII-A geometry chapter 3
Math challengeII-A geometry chapter 3
There seems to be quite a few errors in the sample solution for Problem 3.28. First of all, why is the distance squared from Q to the Focus x^2-(y-p)^2? Shouldn’t it be plus, since the distance is the hypotenuse of this right angle triangle and we should add them up, instead of subtract?
Next, why is the answer 4py=x^2? I did the cancellations and I got 2y^2+2p^2=x^2. Am I right or am I wrong?
Re: Math challengeII-A geometry chapter 3
The distance squared from $Q$ to the focus should be $x^2 + (y-p)^2$, thanks!
Then, setting the two distance squared values equal to each other, $y^2+2py+p^2 = x^2 + y^2 - 2py + p^2$, so the $y^2$ and $p^2$ terms cancel. Simplifying we get $4py = x^2$ which is the parabola.
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