Isabel☺
  • Isabel☺
how will you know if an equation is a parabola, circle, etc.?
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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amistre64
  • amistre64
there is a general conic equation; something like x^2 + xy + y^2 + ... that i can never recall if its a standard conic (not twisted at an angle) you can recognize certain proerties
amistre64
  • amistre64
a parabola only has one square in it a circle will have the same constants for x^2 and y^2, and have a + in the middle an ellipse is like a circle, but it has different constants a hyperbola is like an ellipse, but with a minus sign
Isabel☺
  • Isabel☺
uhmm...kay maybe with some examples? oh, wait thanks! :)

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amistre64
  • amistre64
parabola: y = x^2 + .... circle: x^2 + y^2 = 8 ellipse: 4x^2 + 7y^2 = 15 hyperbola: 3x^2 - 2y^2 = 29
Isabel☺
  • Isabel☺
so why is y=4-x^2 a parabola?
amistre64
  • amistre64
generally, becasue it has one sqaured term in it
Isabel☺
  • Isabel☺
but (x-h)^2 = 4p (y-k) is the eq. of a parabola right?
amistre64
  • amistre64
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amistre64
  • amistre64
there is an algebra definition and a geometric definition; you presented the geometric one
Isabel☺
  • Isabel☺
what's the difference between those definition ?
amistre64
  • amistre64
one is defined by geometric properties, while te other is defined by arithmetical properties. The two are equivalent, but its just the perspective studies that generated them.
amistre64
  • amistre64
directrix distance (directrix is a geometric property) v v (x-h)^2 = 4p (y-k) ^ ^ ^ ^ center x center y
amistre64
  • amistre64
y = 4 -x^2 x^2 = 4 - y (x - 0)^2 = -4/4 (y - 4) p = -1/4; and center (or vertex in this case) is at (0,4)
amistre64
  • amistre64
cost accting exam starting soon, good luck ;)
Isabel☺
  • Isabel☺
thanks! :)

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