Q.416. Equation of the ellipse given its vertices and foci.

Question 146.
Find an equation of an ellipse having veticles (-1, 3),  (7, 3), and foci (0, 3), (6,3).

Answer 146.
Midpoint of vertices or foci, (3, 3) is the center of the ellipse.
Shifting origin to (3, 3),
vertices are (-4, 0) and (4, 0) and
foci are (-3, 0) and (3, 0)
=> a = 4 and ae = 3
=> b^2 = a^2 - (ae)^2 = 16 - 9 = 7
=> eqn. of the ellipse with center, (0, 0) is
x^2/16 + y^2/7 = 1
=> eqn. of the ellipse with center (3, 3) is
(x - 3)^2/16 + (y - 3)^2/7 = 1.

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