What is 7p-p^2=9p+q^2-16-5q^2+6 ?

The solution to 7p-p^2=9p+q^2-16-5q^2+6 is Hyperbola with (h,k)=(-1,0),a=sqrt(11),b=(sqrt(11))/2

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7p-p^2=9p+q^2-16-5q^2+6

7 p - p^{2} = 9 p + q^{2} - 16 - 5 q^{2} + 6

(h, k) = (- 1, 0), a = 11, b = \frac{11}{2}

Solution steps

7 p - p^{2} = 9 p + q^{2} - 16 - 5 q^{2} + 6

Rewrite

7 p - p^{2} - 9 p - q^{2} + 16 + 5 q^{2} - 6 = 0

in the form of a standard hyperbola equation

\frac{( p - ( - 1 ) ) ^{2}}{( 11 ) ^{2}} - \frac{( q - 0 ) ^{2}}{( \frac{11}{2} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 1, 0), a = 11, b = \frac{11}{2}

x^{2} - y^{2} < 8

9 y^{2} - 16 x^{2} = 1

4 x^{2} - 16 y^{2} - 10 x + 21 y - 27 = 0

\frac{x ^{2}}{3} - \frac{y ^{2}}{4} = 1

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

What is 7p-p^2=9p+q^2-16-5q^2+6 ?
The solution to 7p-p^2=9p+q^2-16-5q^2+6 is Hyperbola with (h,k)=(-1,0),a=sqrt(11),b=(sqrt(11))/2