What is 4x^2=10+y^2 ?

The solution to 4x^2=10+y^2 is Hyperbola with (h,k)=(0,0),a=sqrt(5/2),b=sqrt(10)

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4x^2=10+y^2

4 x^{2} = 10 + y^{2}

(h, k) = (0, 0), a = \frac{5}{2}, b = 10

Solution steps

4 x^{2} = 10 + y^{2}

Rewrite

4 x^{2} = 10 + y^{2}

in the form of a standard hyperbola equation

\frac{( x - 0 ) ^{2}}{( \frac{5}{2} ) ^{2}} - \frac{( y - 0 ) ^{2}}{( 10 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = \frac{5}{2}, b = 10

x^{2} - 4 y^{2} - 18 x - 16 y - 35 = 0

\frac{y ^{2} + 3}{4} - \frac{x ^{2} - 1}{5} = 1

y^{2} = 2 x^{2} - 3 x + 4

25 x^{2} - 9 y^{2} - 54 y = 306

16 x^{2} - 9 y^{2} - 96 x + 9 y - 36 = 0

What is 4x^2=10+y^2 ?
The solution to 4x^2=10+y^2 is Hyperbola with (h,k)=(0,0),a=sqrt(5/2),b=sqrt(10)