H(x) = -x^3-2x^2-3x+4; x=2
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The general equation of <span>an ellipse:
we have </span><span>vertices (–4, 2), (2, 2), (–1, –2) and (–1, 6).⇒⇒⇒ red points
by graphing the points ⇒⇒⇒ attached figure 1
the majority axis is the line connecting </span><span>(–1, –2) and (–1, 6) and has a distance = 8
the minority axis is the line connecting </span><span><span>(–4, 2), and (2, 2)</span> and has a distance = 6
(h,k) represents the center of ellipse which is the intersection between axes
∴(h,k) = (-1,2)
and a = 3 , b = 4
∴ the equation of the ellipse is
</span>
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<span>A hyperbola with vertices (9, 3) and (5, 3) ⇒⇒⇒⇒ blue points
and with foci (11, 3) and (3, 3). ⇒⇒⇒⇒ red points
</span><span>by graphing the points ⇒⇒⇒ attached figure 2
</span>so, the hyperbole axis is horizontal
<span>(h,k) represents the center of hyperbola = (7,3) ⇒⇒⇒ green point
a = distance between center and any of vertices = 7 - 5 = 2
c = </span><span>distance between center and any of foci = 7 - 3 = 4
∵ c² = a² + b²
∴ b² = c² - a² = 16 - 4 = 12
the general equation of the hyperbole :
</span><span>
the equation of the </span>hyperbole will be
<span>
</span>
we have </span><span>vertices (–4, 2), (2, 2), (–1, –2) and (–1, 6).⇒⇒⇒ red points
by graphing the points ⇒⇒⇒ attached figure 1
the majority axis is the line connecting </span><span>(–1, –2) and (–1, 6) and has a distance = 8
the minority axis is the line connecting </span><span><span>(–4, 2), and (2, 2)</span> and has a distance = 6
(h,k) represents the center of ellipse which is the intersection between axes
∴(h,k) = (-1,2)
and a = 3 , b = 4
∴ the equation of the ellipse is
</span>
=========================================================
<span>A hyperbola with vertices (9, 3) and (5, 3) ⇒⇒⇒⇒ blue points
and with foci (11, 3) and (3, 3). ⇒⇒⇒⇒ red points
</span><span>by graphing the points ⇒⇒⇒ attached figure 2
</span>so, the hyperbole axis is horizontal
<span>(h,k) represents the center of hyperbola = (7,3) ⇒⇒⇒ green point
a = distance between center and any of vertices = 7 - 5 = 2
c = </span><span>distance between center and any of foci = 7 - 3 = 4
∵ c² = a² + b²
∴ b² = c² - a² = 16 - 4 = 12
the general equation of the hyperbole :
</span><span>
the equation of the </span>hyperbole will be
<span>