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Sagot :
From the equation of the elipse, we have that:
- The endpoints of the major axis are: [tex]x = -4[/tex] and [tex]x = 8[/tex]
- The endpoints of the minor axis are: [tex]y = -3 - \sqrt{24}[/tex] and [tex]y = -3 + \sqrt{24}[/tex].
The equation of an elipse of center [tex](x_0,y_0)[/tex] has the following format:
[tex]\frac{(x - x_0)^2}{a^2} + \frac{(y - y_0)^2}{b^2} = 1[/tex]
If a > b, we have that:
- The endpoints of the major axis are: [tex]x = x_0 \pm a[/tex]
- The endpoints of the minor axis are: [tex]y = y_0 \pm b[/tex]
In this problem, the equation is:
[tex]\frac{(x - 2)^2}{36} + \frac{(y + 3)^2}{24} = 1[/tex]
Thus [tex]x_0 = 2, y_0 = -3, a = 6, b = \sqrt{24}[/tex]
For the major axis:
[tex]x = x_0 \pm a[/tex]
[tex]x = 2 \pm 6[/tex]
[tex]x = 2 - 6 = -4[/tex]
[tex]x = 2 + 6 = 8[/tex]
The endpoints of the major axis are: [tex]x = -4[/tex] and [tex]x = 8[/tex]
For the minor axis:
[tex]y = y_0 \pm b[/tex]
[tex]y = -3 \pm \sqrt{24}[/tex]
[tex]y = -3 - \sqrt{24}[/tex]
[tex]y = -3 + \sqrt{24}[/tex]
The endpoints of the minor axis are: [tex]y = -3 - \sqrt{24}[/tex] and [tex]y = -3 + \sqrt{24}[/tex].
A similar problem is given at https://brainly.com/question/21405803
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