SOLUTION: write each equation in standard form.Identify the related conic. y-4y=4x+16 x^2+y^2-8x-24y=9 x^2=y^2+20x-10y+4=0

Question 428097: write each equation in standard form.Identify the related conic.
y-4y=4x+16
x^2+y^2-8x-24y=9
x^2=y^2+20x-10y+4=0
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
write each equation in standard form.Identify the related conic.
y-4y=4x+16
x^2+y^2-8x-24y=9
x^2=y^2+20x-10y+4=0
..
y-4y=4x+16
-3y=4x+15
y=-4/3x-3
This is a straight line of the form, y=mx+b.with slope = -4/3, and y-intercept=-3
..
x^2+y^2-8x-24y=9
completing the squares
(x^2-8x+16)+(y^2-24y+144)=-9+16+144=151
(x-4)^2+(y-12)^2=151
divide by 151
(x-4)^2+(y-12)^2=151
This is a circle with center at (4,12) and radius=sqrt(151 )=12.29..
..
x^2=y^2+20x-10y+4=0
me thinks the equal sign was meant to be a minus sign
x^2-y^2+20x-10y+4=0
completing the squares
(x^2+20x+100)-(y^2+10y+25)=-4+100-25=71
(x+10)^2-(y+5)^2=71
This is a hypebola with center at (-10,-5) and a horizontal transverse axis (opens sideways)
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