What is 4x^2+16y^2-64=0 ?

The solution to 4x^2+16y^2-64=0 is Ellipse with (h,k)=(0,0),a=4,b=2

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4x^2+16y^2-64=0

4 x^{2} + 16 y^{2} - 64 = 0

(h, k) = (0, 0), a = 4, b = 2

Solution steps

4 x^{2} + 16 y^{2} - 64 = 0

Rewrite

4 x^{2} + 16 y^{2} - 64 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 4, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 4, b = 2

\frac{x ^{2}}{12} + \frac{y ^{2}}{80} = 1

4 x^{2} + 25 y^{2} = 1

x^{2} - 6 x + 4 y^{2} + 8 y - 3 = 0

\frac{( x - 3 ) ^{2}}{49} + \frac{( y + 5 ) ^{2}}{25} = 1

2 x^{2} - 12 x + y^{2} + 6 y + 26 = 0

What is 4x^2+16y^2-64=0 ?
The solution to 4x^2+16y^2-64=0 is Ellipse with (h,k)=(0,0),a=4,b=2