SOLUTION: Write the equation of the center at point (-2,3) and cruve passing through points (-2,0) and (2,3). Write the equation of the hyperbola with center at the origin, passting thour

Question 89902: Write the equation of the center at point (-2,3) and cruve passing through points (-2,0) and (2,3).
Write the equation of the hyperbola with center at the origin, passting thourhg the points (-2,0) and (2,0) having a focus at (4,0)

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Write the equation of the center at point (-2,3) and cruve passing through points (-2,0) and (2,3).
If you plot those points you see the curve cannot be a circle, hyperbola, or
a parabola; it must be an ellipse.
Form if Center at (-2,3):
(x+2)^2/a^2 + (y-3)^2/b^2 = 1
Distance from center to (2,3) = 4 = a
Distance from center to (-2,0) = 2 = b
-----------
EQUATION:
(x+2)^2/16 + (y-3)^2/4 = 1
========================
Write the equation of the hyperbola with center at the origin, passing through the points (-2,0) and (2,0) having a focus at (4,0)
-----------
Plot the points
Form of the hyperbola with center at (0,0):
x^2/a^2 - y^2/b^2 = 1
a = distance from center to vertex = 2
c = distance from center to focus = 4
--------
For a hyperbola c^2 = a^2+b^2
16 = 4 + b^2
b^2 = 12
------------
EQUATION:
x^2/4 - y^2/12 = 1
=================
Cheers,
Stan H.

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