Author Topic: Need help with Q (Read 739 times) Tweet Share

Steven Haneul · « **on:** October 22, 2017, 06:19:01 pm »

Hey! I need help with the entire question.
Thanks heaps

jamonwindeyer · « **Reply #1 on:** October 22, 2017, 06:50:21 pm »

Quote from: Steven Haneul on October 22, 2017, 06:19:01 pm

Hey! I need help with the entire question.
Thanks heaps

Hey! First step is to solve these equations simulteneouslly to find the POI, I'll use the elimination method:

$\left(y-c\right)^2=r^2-y\\y^2-2cy+c^2=r^2-y\\y^2+(1-2c)y+(c^2-r^2)=0$

Now we know there are two POI, but they have the same y-coordinate. So, this quadratic only has a single solution. Therefore, $\Delta=0$:

$\Delta=b^2-4ac=0\$1-2c)^2-4c^2+4r^2=0\\1-4c+4r^2=0\\4c=1+4r^2$

Now the solution itself (using the quadratic formula) takes the form:

$y=\frac{-(1-2c)\pm0}{2}$

Remember \(\Delta=0$ so the square root part of the formula is 0! Now, we need these to occur at a value in the upper half of the plane based on the diagram. That is, $y>0$:

$\frac{-1+2c}{2}>0\\-1+2c>0\\c>\frac{1}{2}$

This is a super tough question to interpret, does this help? I moved quick so let me know if I can elaborate

RuiAce · « **Reply #2 on:** October 22, 2017, 06:56:31 pm »

It was already done in the compilation so a tiny bit more elaboration can be found there

Steven Haneul · « **Reply #3 on:** October 22, 2017, 07:24:08 pm »

Yee it all makes sense! Thanks Jamon and Rui!

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Author Topic: Need help with Q (Read 739 times) Tweet Share

Steven Haneul

Need help with Q

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Steven Haneul

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