What is x^2+4y^2-64=0 ?

The solution to x^2+4y^2-64=0 is Ellipse with (h,k)=(0,0),a=8,b=4

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x^2+4y^2-64=0

x^{2} + 4 y^{2} - 64 = 0

(h, k) = (0, 0), a = 8, b = 4

Solution steps

x^{2} + 4 y^{2} - 64 = 0

Rewrite

x^{2} + 4 y^{2} - 64 = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{8 ^{2}} + \frac{( y - 0 ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 8, b = 4

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 8, b = 4

\frac{x ^{2}}{5} + \frac{y ^{2}}{8} = 1

\frac{x ^{2}}{140} + \frac{( y - 6 ) ^{2}}{4} = 1

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

9 x^{2} - 54 x + 4 y^{2} = - 45

x^{2} + 3 y^{2} + x - 2 y - 1 = 0

What is x^2+4y^2-64=0 ?
The solution to x^2+4y^2-64=0 is Ellipse with (h,k)=(0,0),a=8,b=4