What is x^2+(x+3)^2=y^2 ?

The solution to x^2+(x+3)^2=y^2 is Hyperbola with (h,k)=(-3/2 ,0),a= 3/(sqrt(2)),b= 3/2

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x^2+(x+3)^2=y^2

x^{2} + (x + 3)^{2} = y^{2}

(h, k) = (- \frac{3}{2}, 0), a = \frac{3}{2}, b = \frac{3}{2}

Solution steps

x^{2} + (x + 3)^{2} = y^{2}

Rewrite

x^{2} + (x + 3)^{2} - y^{2} = 0

in the form of a standard hyperbola equation

\frac{( y - 0 ) ^{2}}{( \frac{3}{2} ) ^{2}} - \frac{( x - ( - \frac{3}{2} ) ) ^{2}}{( \frac{3}{2} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- \frac{3}{2}, 0), a = \frac{3}{2}, b = \frac{3}{2}

4 x^{2} - 34 y - 5 y^{2} - 36 = 0

(\frac{2 y - 3 x}{18}) (\frac{2 y + 3 x}{2}) = 1

x^{2} - 2 y^{2} = 7

x^{2} - 2 y^{2} = 2

4 y^{2} - 9 x^{2} + 40 y - 540 x - 8036 = 0

What is x^2+(x+3)^2=y^2 ?
The solution to x^2+(x+3)^2=y^2 is Hyperbola with (h,k)=(-3/2 ,0),a= 3/(sqrt(2)),b= 3/2