Question

: Graph the following ellipse shown below

(x-5)^2 (y+2)^2
--------- + ---------- = 1
9 25

Answer 1

Answer on Question #57275 – Math – Analytic Geometry

Question

Graph the following ellipse shown below

$$\frac {(x - 5) ^ {2}}{9} + \frac {(y + 2) ^ {2}}{25} = 1.$$

Solution

The equation of an ellipse is

$$\frac {(x - x _ {0}) ^ {2}}{a ^ {2}} + \frac {(y - y _ {0}) ^ {2}}{b ^ {2}} = 1$$

where

$(x_0, y_0)$ is the center.

If $b > a$, then $a, b$ are lengths of minor and major semiaxes respectively.

If $a > b$, then $b, a$ are lengths of minor and major semiaxes respectively.

In our case we have

$$\begin{array}{l} (x _ {0}, y _ {0}) = (5, - 2); \\ a = 3; \\ b = 5; \\ b > a. \end{array}$$

Thus, we get

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