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

The solution to 16x^2+y^2=64 is Ellipse with (h,k)=(0,0),a=2,b=8

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16x^2+y^2=64

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

(h, k) = (0, 0), a = 2, b = 8

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 2, b = 8

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 8, a = 2

\frac{( x - 3 ) ^{2}}{16} + \frac{( y + 1 ) ^{2}}{25} = 1

\frac{( x - 3 ) ^{2}}{25} + \frac{( y - 2 ) ^{2}}{9} = 1

4 x^{2} + 9 y^{2} - 24 x + 72 y + 144 = 0

4 x^{2} + 9 y^{2} + 24 x + 18 y + 9 = 0

x^{2} + 5 y^{2} = 2

What is 16x^2+y^2=64 ?
The solution to 16x^2+y^2=64 is Ellipse with (h,k)=(0,0),a=2,b=8