Question

10. Write an equation of the ellipse with foci at (0, ±11) and vertices at (0, +12).

+
144 265
x²
265
+
2/2
x²
+
144 23
+
y²
144
= 1
32
144
M
-1
P 1

Answer 1

x²/23 +y²/144 = 1

Explanation:

You want an equation of the ellipse with foci at (0, ±11) and a vertex at (0, 12).

Minor axis

The given vertex is in line with the foci, so represents one end of the major axis. The length of the semi-minor axis will be ...

a = √(b² -f²) . . . . . . where f is the center-to-focus distance

a = √(12² -11²) = √(144 -121) = √23

Equation

The equation is ...

x²/a² +y²/b² = 1

x²/23 +y²/144 = 1

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