Solve 25x^2=64+16y^2

Question

25 x^{2} = 64 + 16 y^{2}

Identify the conic

Find the standard equation of the hyperbola

Find the center of the hyperbola

Find the foci of the hyperbola

\frac{x ^{2}}{\frac{64}{25}} - \frac{y ^{2}}{4} = 1

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Solve the equation

$Solve for x$

$Solve for y$

x = \frac{4 4 + y ^{2}}{5} x = - \frac{4 4 + y ^{2}}{5}

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Testing for symmetry

Testing for symmetry about the origin

Testing for symmetry about the x-axis

Testing for symmetry about the y-axis

Symmetry with respect to the origin

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Find the first derivative

$Find the derivative with respect to x$

$Find the derivative with respect to y$

\frac{d y}{d x} = \frac{25 x}{16 y}

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Find the second derivative

$Find the second derivative with respect to x$

$Find the second derivative with respect to y$

\frac{d ^{2} y}{d x ^{2}} = \frac{400 y ^{2} - 625 x ^{2}}{256 y ^{3}}

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Rewrite the equation

Rewrite in polar form

r = \frac{8 41 cos ^{2} ( θ ) - 16}{∣ 41 cos ^{2} ( θ ) - 16 ∣} r = - \frac{8 41 cos ^{2} ( θ ) - 16}{∣ 41 cos ^{2} ( θ ) - 16 ∣}

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25x^2=64+16y^2

Identify the conic

Find the standard equation of the hyperbola

Find the center of the hyperbola

Find the foci of the hyperbola

Solve the equation

Solve for x

Solve for y

Testing for symmetry

Testing for symmetry about the origin

Testing for symmetry about the x-axis

Testing for symmetry about the y-axis

Find the first derivative

Find the derivative with respect to x

Find the derivative with respect to y

Find the second derivative

Find the second derivative with respect to x

Find the second derivative with respect to y

Rewrite the equation

Rewrite in polar form

Graph

$Solve for x$

$Solve for y$

$Find the derivative with respect to x$

$Find the derivative with respect to y$

$Find the second derivative with respect to x$

$Find the second derivative with respect to y$