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Answer:
(ii) center: (-3, 6)
(iii) A(-3, 6-√51), B(7, 6), D(-3, 6+√51), H(-13, 6)
(iv) (x +3)²/100 +(y -6)²/51 = 1
Step-by-step explanation:
(ii) The center is the midpoint between the foci:
center = ((-10, 6) +(4, 6))/2 = (-10+4, 6+6)/2
center = (-3, 6)
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(iii) The vertices are the center plus or minus the semi-major axis length in the x-direction: (-3±10, 6).
The semi-minor axis length is the root of the difference of squares of the semi-major axis and the center-focus distance:
semi-minor axis = √(10² -7²)
semi-minor axis = √51
So, the co-vertices are the center plus or minus this value in the y-direction: (-3, 6±√51)
Using the labeling in the drawing the various points are ...
A(-3, 6-√51), B(7, 6), D(-3, 6+√51), H(-13, 6)
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(iv) For center (h, k) and semi-axis lengths 'a' and 'b' the equation of an ellipse is ...
(x -h)²/a² +(y -k)²/b² = 1
For the center and axes here, the equation is ...
(x +3)²/100 +(y -6)²/51 = 1
