What is x^2+4y^2-4x-8y-92=0 ?

The solution to x^2+4y^2-4x-8y-92=0 is Ellipse with (h,k)=(2,1),a=10,b=5

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x^2+4y^2-4x-8y-92=0

x^{2} + 4 y^{2} - 4 x - 8 y - 92 = 0

(h, k) = (2, 1), a = 10, b = 5

Solution steps

x^{2} + 4 y^{2} - 4 x - 8 y - 92 = 0

Rewrite

x^{2} + 4 y^{2} - 4 x - 8 y - 92 = 0

in the form of the standard ellipse equation

\frac{( x - 2 ) ^{2}}{1 0 ^{2}} + \frac{( y - 1 ) ^{2}}{5 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2, 1), a = 10, b = 5

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (2, 1), a = 10, b = 5

\frac{x ^{2}}{5 ^{2}} + \frac{y ^{2}}{4 ^{2}} = 1

\frac{( x - 2 ) ^{2}}{16} + \frac{( y + 3 ) ^{2}}{9} = 1

7 x^{2} + 16 y^{2} = 112

2 x^{2} + 10 y^{2} + 10 x - 6 y - 10 = 0

x^{2} + y^{2} - 4 y \leq 0

What is x^2+4y^2-4x-8y-92=0 ?
The solution to x^2+4y^2-4x-8y-92=0 is Ellipse with (h,k)=(2,1),a=10,b=5