anonymous
  • anonymous
Find an equation in standard form for the hyperbola with vertices at (0, ±3) and foci at (0, ±7)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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jdoe0001
  • jdoe0001
so, I gather you know the equation of a hyperbola?
jdoe0001
  • jdoe0001
well @n14r96 the vertices are at (0, +3) and (0, -3) the "x" doesn't change the "y" does meaning is going upwards, thus is a vertical traversal axis
jdoe0001
  • jdoe0001
the distance from one vertex to the other is 3+3, so 6 half-way through is the (h,k) center the distance for the "a" element in the formula is the distance from the center to the vertex so the vertices are at (0, +3) and (0, -3), so the "a" distance is 3 so a = 3 the foci are at (0, ±7) the distance from the center to a focus is "c" you center is at (0,0) your foci at (0, ±7) so the "c" distance is 7 c = 7 so, what about "b"? \(c^2=a^2+b^2 \implies 7^2 = 3^2+b^2\) solve for \(b^2\) the equation uses \(a^2 \ and \ b^2\) so since a = 3, \(a^2 = 9\)

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jdoe0001
  • jdoe0001
and of course, your center is at (0,0)
anonymous
  • anonymous
so y^2/49-x^2/9=1 ???

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