What is pi(a^2-b^2)=(49pi)/2 ?

The solution to pi(a^2-b^2)=(49pi)/2 is Hyperbola with (h,k)=(0,0),a= 7/(sqrt(2)),b= 7/(sqrt(2))

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pi(a^2-b^2)=(49pi)/2

π (a^{2} - b^{2}) = \frac{49 π}{2}

(h, k) = (0, 0), a = \frac{7}{2}, b = \frac{7}{2}

Solution steps

π (a^{2} - b^{2}) = \frac{49 π}{2}

Rewrite

π (a^{2} - b^{2}) = \frac{49 π}{2}

in the form of a standard hyperbola equation

\frac{( a - 0 ) ^{2}}{( \frac{7}{2} ) ^{2}} - \frac{( b - 0 ) ^{2}}{( \frac{7}{2} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = \frac{7}{2}, b = \frac{7}{2}

a^{2} - b^{2} = 891

\frac{( x + 2 ) ^{2}}{10} - \frac{( y + 4 ) ^{2}}{25} = 1

\frac{( x + 3 ) ^{2}}{4} - \frac{( y - 2 ) ^{2}}{2} = 2

x^{2} - 4 y^{2} + 16 = 0

9 x^{2} - 54 x + 9 - 4 y^{2} - 8 y - 113 = 0

What is pi(a^2-b^2)=(49pi)/2 ?
The solution to pi(a^2-b^2)=(49pi)/2 is Hyperbola with (h,k)=(0,0),a= 7/(sqrt(2)),b= 7/(sqrt(2))