What is 100x^2+4y^2+1200x-32y+3264=0 ?

The solution to 100x^2+4y^2+1200x-32y+3264=0 is Ellipse with (h,k)=(-6,4),a=2,b=10

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100x^2+4y^2+1200x-32y+3264=0

100 x^{2} + 4 y^{2} + 1200 x - 32 y + 3264 = 0

(h, k) = (- 6, 4), a = 2, b = 10

Solution steps

100 x^{2} + 4 y^{2} + 1200 x - 32 y + 3264 = 0

Rewrite

100 x^{2} + 4 y^{2} + 1200 x - 32 y + 3264 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 6 ) ) ^{2}}{2 ^{2}} + \frac{( y - 4 ) ^{2}}{1 0 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 6, 4), a = 2, b = 10

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 6, 4), b = 10, a = 2

16 x^{2} + 15 y^{2} - 64 x - 90 y - 41 = 0

25 y^{2} + 9 x^{2} - 108 x - 200 y + 499 = 0

50 = \frac{100}{1 + x ^{2} + y ^{2}}

9 x^{2} + 4 y^{2} - 36 x + 8 y + 31 = 0

\frac{x ^{2}}{1.586 9 ^{2}} + \frac{y ^{2}}{0.9989 8 ^{2}} = 1

What is 100x^2+4y^2+1200x-32y+3264=0 ?
The solution to 100x^2+4y^2+1200x-32y+3264=0 is Ellipse with (h,k)=(-6,4),a=2,b=10