Question

: Graph the equations shown below, the graph is scaled 9 high and 9 wide.


X^2 y^2
----- + ------- = 1
20 20

6x^2 + 6y^2 = 144

x^2 + y^2 = 16

20x^2 – 20y^2 = 400

Answer 1

Answer on Question #57351 – Math – Analytic Geometry

Question

Graph the equations shown below, the graph is scaled 9 high and 9 wide.

$$\begin{array}{l l} X ^ {\wedge} 2 & y ^ {\wedge} 2 \\ \dots \dots + & \dots \dots = 1 \\ 2 0 & 2 0 \end{array}$$ $$6 x ^ {\wedge} 2 + 6 y ^ {\wedge} 2 = 1 4 4$$ $$x ^ {\wedge} 2 + y ^ {\wedge} 2 = 1 6$$ $$2 0 x ^ {\wedge} 2 - 2 0 y ^ {\wedge} 2 = 4 0 0$$

Solution

1. $\frac{x^2}{20} + \frac{y^2}{20} = 1$ is a circle centered on $(0,0)$ and with radius of $\sqrt{20} = 2\sqrt{5}$ .

2. $6x^{2} + 6y^{2} = 144$ is a circle centered on $(0,0)$ and with radius of $\sqrt{\frac{144}{6}} = \frac{12}{\sqrt{6}} = 2\sqrt{6}$ .

3. $x^{2} + y^{2} = 16$ is a circle centered on $(0,0)$ and with radius of 4.

4. $20x^{2} - 20y^{2} = 400$ is a hyperbola centered on $(0,0)$ with the horizontal transverse axis, $a = b = \sqrt{20} = 2\sqrt{5}$ .

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