What is 16x^2+4y^2+96x-8y+84=0 ?

The solution to 16x^2+4y^2+96x-8y+84=0 is Ellipse with (h,k)=(-3,1),a=2,b=4

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16x^2+4y^2+96x-8y+84=0

16 x^{2} + 4 y^{2} + 96 x - 8 y + 84 = 0

(h, k) = (- 3, 1), a = 2, b = 4

Solution steps

16 x^{2} + 4 y^{2} + 96 x - 8 y + 84 = 0

Rewrite

16 x^{2} + 4 y^{2} + 96 x - 8 y + 84 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 3, 1), a = 2, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 3, 1), b = 4, a = 2

What is 16x^2+4y^2+96x-8y+84=0 ?
The solution to 16x^2+4y^2+96x-8y+84=0 is Ellipse with (h,k)=(-3,1),a=2,b=4