Question

Find an equation in standard form for the ellipse with the vertical major axis of length 18, and minor axis of length 16.

Answer 1

Answer on Question #45378 – Math – Analytical Geometry

Find an equation in standard form for the ellipse with the vertical major axis of length 18, and minor axis of length 16.

Solution:

Given equation is that of an ellipse with a vertical major axis. Its standard form:

$$\frac{(x - h)^2}{b^2} + \frac{(y - k)^2}{a^2} = 1, \, a > b, \, (h, k) = (x, y) \text{ coordinates of center.}$$

Given center: $(0,0)$

Given length of vertical major axis $= 18 = 2a$

$$a = 9$$ $$a^2 = 81$$ $$\text{given length of minor axis} = 16 = 2b$$ $$b = 8$$ $$b^2 = 64$$

Equation:

$$\frac{x^2}{64} + \frac{y^2}{81} = 1$$

Answer: $\frac{x^2}{64} + \frac{y^2}{81} = 1$

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