What is Janelle’s position relative to sea level while swimming? What should the altimeter read at this position?

What is Janelle’s position relative to sea level while swimming? What should the altimeter read at

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photon22

05.09.2020

Mathematics

The standard form of the ellipse is $\frac{x^{2}}{25} +\frac{y^{2}}{169} = 1$ . Coordinates of the foci are $F_{1} (x,y) = (0,-c)$ and $F_{2}(x,y) = (0,c)$ , respectively.

Step-by-step explanation:

The equation of a ellipse centered in the origin in standard form is defined by following formula:

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

Where a, b are the coefficients of the ellipse.

Now we proceed to transform the equation of the ellipse in general form into standard form by algebraic means:

$169\cdot x^{2}+25\cdot y^{2}-4225 = 0$

$169\cdot x^{2}+25\cdot y^{2} = 4225$

$\frac{x^{2}}{25} +\frac{y^{2}}{169} = 1$

Since b a , then major axis of the ellipse is located in y-axis. The distance between center and focus () is calculated by following Pythagorean identity:

$c =\sqrt{b^{2}-a^{2}}$ (2)

c = 12

The location of the foci are represented by $F_{1} (x,y) = (0,-c)$ and $F_{2}(x,y) = (0,c)$ . If we know that c = 12 , then the location of the foci are, respectively:

$F_{1}(x,y) = (0,-12)$ , $F_{2}(x,y) = (0,12)$

Put the equation 169x^2+25y^2-4225=0 in standard form and sketch the ellipse including the foci in y

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