What is 16(x-8)^2+64(y-4)^2=1024 ?

The solution to 16(x-8)^2+64(y-4)^2=1024 is Ellipse with (h,k)=(8,4),a=8,b=4

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16(x-8)^2+64(y-4)^2=1024

16 (x - 8)^{2} + 64 (y - 4)^{2} = 1024

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

Solution steps

16 (x - 8)^{2} + 64 (y - 4)^{2} = 1024

Rewrite

16 (x - 8)^{2} + 64 (y - 4)^{2} = 1024

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

1 x^{2} + 4 y^{2} + 9 x + 9 y - 9 = 0

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

25 x^{2} + 9 y^{2} + 50 x - 54 y - 119 = 0

\frac{( x - 0.5 ) ^{2}}{10} + \frac{( y - 3 ) ^{2}}{5} = 1

\frac{x ^{2}}{9} + \frac{y ^{2}}{40} = 1

What is 16(x-8)^2+64(y-4)^2=1024 ?
The solution to 16(x-8)^2+64(y-4)^2=1024 is Ellipse with (h,k)=(8,4),a=8,b=4