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

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

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16x^2+4y^2=64

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

8 x^{2} + 2 y^{2} + 16 x = 0

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

\frac{x ^{2}}{16} + \frac{( y + 1 ) ^{2}}{4} - 1 = 0

\frac{( x ^{2} )}{25} + \frac{( y ^{2} )}{9} = 1

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

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