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# find conic and rewrite in simple form

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-y^2 + x + 20y - 94 = 0

Guest Mar 27, 2015

#2
+92805
+10

Thanks Alan,

I will do some of what Alan did only a little slower

$$\\-y^2 + x + 20y - 94 = 0\\\\ Mult both sides by -1 \\\\ y^2 - x - 20y + 94 = 0\\\\ y^2 - 20y- x =\;-94\\\\ (y^2 - 20y+(\frac{-20}{2})^2)- x =\;-94+(\frac{-20}{2})^2)\\\\ (y^2 - 20y+100)- x =\;-94+100\\\\ (y-10)^2- x =\;6\\\\ (y-10)^2 =\;x+6\\\\$$

this is sideways parabola that opens out in the positive direction.

I know it is a parabola because one of the varibables is squared but not the other.  And both are on the top and they are not multiplied together or anything strange like that.

I know it is sideways because it is the y that is squared, not the x.

I know it opens out in the positive direction because the number in front of the y^2 is an invisable 1 and it is Positive

I can see that the vertex is (-6,10)

I can see other things too but that might be enough for now.  Alan's graph will hopefully backup everything that I have said. :)

PS.  There was a small error      that i have fixed.  Thanks Alan

Melody  Mar 27, 2015
#1
+26753
+10

This can be re-written as (y - 10)2 = x + 6,  so y = 10 ± √(x + 6)

This is a parabola.

.

Alan  Mar 27, 2015
#2
+92805
+10

Thanks Alan,

I will do some of what Alan did only a little slower

$$\\-y^2 + x + 20y - 94 = 0\\\\ Mult both sides by -1 \\\\ y^2 - x - 20y + 94 = 0\\\\ y^2 - 20y- x =\;-94\\\\ (y^2 - 20y+(\frac{-20}{2})^2)- x =\;-94+(\frac{-20}{2})^2)\\\\ (y^2 - 20y+100)- x =\;-94+100\\\\ (y-10)^2- x =\;6\\\\ (y-10)^2 =\;x+6\\\\$$

this is sideways parabola that opens out in the positive direction.

I know it is a parabola because one of the varibables is squared but not the other.  And both are on the top and they are not multiplied together or anything strange like that.

I know it is sideways because it is the y that is squared, not the x.

I know it opens out in the positive direction because the number in front of the y^2 is an invisable 1 and it is Positive

I can see that the vertex is (-6,10)

I can see other things too but that might be enough for now.  Alan's graph will hopefully backup everything that I have said. :)

PS.  There was a small error      that i have fixed.  Thanks Alan

Melody  Mar 27, 2015