What is 4x^2+16y^2-16x-96y+96=0 ?

The solution to 4x^2+16y^2-16x-96y+96=0 is Ellipse with (h,k)=(2,3),a=4,b=2

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4x^2+16y^2-16x-96y+96=0

4 x^{2} + 16 y^{2} - 16 x - 96 y + 96 = 0

(h, k) = (2, 3), a = 4, b = 2

Solution steps

4 x^{2} + 16 y^{2} - 16 x - 96 y + 96 = 0

Rewrite

4 x^{2} + 16 y^{2} - 16 x - 96 y + 96 = 0

in the form of the standard ellipse equation

\frac{( x - 2 ) ^{2}}{4 ^{2}} + \frac{( y - 3 ) ^{2}}{2 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2, 3), a = 4, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (2, 3), a = 4, b = 2

17 x^{2} + 16 y^{2} - 102 x - 32 y - 103 = 0

x^{2} - 4 x + 100 y^{2} + 200 y + 4 = 0

2 y - xx - yy > 0

2 x^{2} + 4 y^{2} + 8 x + 9 y - 3 = 0

25 x^{2} + 9 y^{2} - 100 x - 54 y - 44 = 0

What is 4x^2+16y^2-16x-96y+96=0 ?
The solution to 4x^2+16y^2-16x-96y+96=0 is Ellipse with (h,k)=(2,3),a=4,b=2