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When you plot the given points on a coordinate plane, you can see this is an ellipse that is vertical.  The equation for this is [tex] \frac{(x-h) ^{2} }{ b^{2} }+ \frac{(y-k) ^{2} }{ a^{2} }=1 [/tex].  Of the values a and b, a is always greater than b, so it is on our major axis, the y-axis (it's under the y-k).  a is the distance from the center to the vertices.  When you plotted those given points, you can see that point dead center between the foci and the vertices is the origin (0, 0).  That gives us our h and k values of 0 and 0.  a is the number of units from the h coordinate of 0 to the y coordinate of the vertex, so a = 12.  c is the number of units from the center to the foci, so c = 11.  We need to find b now using the formula for the foci which is [tex] c^{2} = a^{2}- b^{2} [/tex].  We have c and a, so [tex]121=144- b^{2} [/tex] and [tex]b= \sqrt{23} [/tex].  Now we have all the info we need to rewrite the equation: [tex] \frac{(x-0) ^{2} }{23} + \frac{(y-0) ^{2} }{144}=1 [/tex] or, simplified, [tex] \frac{ x^{2} }{23} + \frac{ y^{2} }{144}=1 [/tex]

The equation of the ellipse with the given parameters is; (x²/23) +  (y²/144) = 1

What is the Equation of the Ellipse?

Since the vertices are at (0 ± 12), then it means that the ellipse given as a vertical major axis at (a = 12). Thus, taking the ellipse with its center at the origin, we will get the general equation:

(x²/b²) +  (y²/a²) = 1

Since the foci is at (0 ± 11), then it means that the distance from the center of the ellipse to the focus is c = 11. Thus, the value of b, the minor radius is gotten from;

c² = a² - b²

b = √(a² - c²)

b = √(12² - 11²)

b = √23

Thus;

a² = 144

b² = 23

Equation of the ellipse is;

(x²/23) +  (y²/144) = 1

Read more about equation of ellipse at; https://brainly.com/question/16904744