toxicsugar22
  • toxicsugar22
12x^2-3y^2+24y-84=0 give the exact coordinates of any four points on the hyperbola
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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toxicsugar22
  • toxicsugar22
hi can u help me
dumbcow
  • dumbcow
if x=0 -3y^2 +24y -84 =0 factor out a -3 y^2 -8y + 28 =0 b^2 -4ac < 0, complex solutions if y=0 12x^2 = 84 x^2 = 7 x = +-sqrt(7) that gives 2 points get x by itself 12x^2 = 3y^2 -24y +84 x^2 = 1/4y^2 - 2y +7 x = sqrt[1/4y^2 -2y +7] pick 2 y_values y=1 --> x =+- sqrt(21/4) = +-sqrt(21)/2 there are other 2 points
amistre64
  • amistre64
12x^2 -3(y^2 +8y +____) = 84 -3(___) 12x^2 -3(y^2 +8y +16) = 84 -3(16) 12x^2 -3(y-4)^2 = 84 -48 = 36 12/36 x^2 -3/36(y-4)^2 = 1 x^2 (y-4)^2 --- - ------ = 1 3 12

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toxicsugar22
  • toxicsugar22
ok can u help me with one more
amistre64
  • amistre64
(sqrt(3), 0) (-sqrt(3),0) are 2 that i get
amistre64
  • amistre64
that might nota worked out ....
toxicsugar22
  • toxicsugar22
yeah
amistre64
  • amistre64
i think i got lost trying to type it all in :)
toxicsugar22
  • toxicsugar22
ok
toxicsugar22
  • toxicsugar22
but can u help me
anonymous
  • anonymous
once you have \[\frac{x^2}{3}-\frac{(y-4)^2}{12}=1\] cant you just pick y and solve for x?
toxicsugar22
  • toxicsugar22
y =0
toxicsugar22
  • toxicsugar22
lets both try that together can u please show me
anonymous
  • anonymous
say for example \[y=2\] \[\frac{x^2}{3}-\frac{4}{12}=1\]
toxicsugar22
  • toxicsugar22
ok
anonymous
  • anonymous
\[\frac{x^2}{3}=1+\frac{4}{12}=1+\frac{1}{3}=\frac{4}{3}\]
dumbcow
  • dumbcow
i already gave you 4 points
anonymous
  • anonymous
\[x^2=4\] \[x=\pm 2\]
anonymous
  • anonymous
or you can pick any other y to solve for x.
toxicsugar22
  • toxicsugar22
so that is one point
anonymous
  • anonymous
actually 2: \[(-2,4)\] and \[(2,4)\]
dumbcow
  • dumbcow
(+-sqrt(7), 0) (+-sqrt(21)/2, 1) (+-2, 2) there are 6 points
anonymous
  • anonymous
let y = 1 \[\frac{x^2}{3}-\frac{(1-4)^2}{12}=1\] \[\frac{x^2}{3}-\frac{9}{12}=1\] \[\frac{x^2}{3}=1+\frac{9}{12}=1+\frac{3}{4}=\frac{7}{4}\]
anonymous
  • anonymous
so \[x^2=\frac{21}{4}\] \[x=\pm \frac{\sqrt{21}}{2}\]
anonymous
  • anonymous
got it?

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