What is x^2+5y^2-4x-16=0 ?

The solution to x^2+5y^2-4x-16=0 is Ellipse with (h,k)=(2,0),a=2sqrt(5),b=2

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x^2+5y^2-4x-16=0

x^{2} + 5 y^{2} - 4 x - 16 = 0

(h, k) = (2, 0), a = 25, b = 2

Solution steps

x^{2} + 5 y^{2} - 4 x - 16 = 0

Rewrite

x^{2} + 5 y^{2} - 4 x - 16 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, 0), a = 25, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (2, 0), a = 25, b = 2

4 x^{(2)} + y^{(2)} = 36

9 x^{2} + 25 y^{2} - 36 x - 50 y + 52 = 0

64 x^{2} + 81 y^{2} = 5184

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

2 x^{2} + 24 y^{2} + 6 x + 4 y + 1 > 0

What is x^2+5y^2-4x-16=0 ?
The solution to x^2+5y^2-4x-16=0 is Ellipse with (h,k)=(2,0),a=2sqrt(5),b=2