What is 7^2+b^2=(c+1)^2 ?

The solution to 7^2+b^2=(c+1)^2 is Hyperbola with (h,k)=(0,-1),a=7,b=7

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7^2+b^2=(c+1)^2

7^{2} + b^{2} = (c + 1)^{2}

(h, k) = (0, - 1), a = 7, b = 7

Solution steps

7^{2} + b^{2} = (c + 1)^{2}

Rewrite

7^{2} + b^{2} - (c + 1)^{2} = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (0, - 1), a = 7, b = 7

- 16 x^{2} + 9 y^{2} - 144 = 0

4 y^{2} - 2 x^{2} + 24 y - 8 x - 9 = 0

4 x^{2} - y^{2} - 8 x + 6 y - 4 = 0

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

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

What is 7^2+b^2=(c+1)^2 ?
The solution to 7^2+b^2=(c+1)^2 is Hyperbola with (h,k)=(0,-1),a=7,b=7