What is 5x^2+y^2-20x+19=0 ?

The solution to 5x^2+y^2-20x+19=0 is Ellipse with (h,k)=(2,0),a=sqrt(1/5),b=1

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5x^2+y^2-20x+19=0

5 x^{2} + y^{2} - 20 x + 19 = 0

(h, k) = (2, 0), a = \frac{1}{5}, b = 1

Solution steps

5 x^{2} + y^{2} - 20 x + 19 = 0

Rewrite

5 x^{2} + y^{2} - 20 x + 19 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, 0), a = \frac{1}{5}, b = 1

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, 0), b = 1, a = \frac{1}{5}

\frac{( x + 2 ) ^{2}}{16} + \frac{( y - 3 ) ^{2}}{4} = 1

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

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

\frac{( x + 1 ) ^{2}}{4} + \frac{( y - 2 ) ^{2}}{9} = 1

16 x^{2} - 64 x + 25 y^{2} + 150 y = 111

What is 5x^2+y^2-20x+19=0 ?
The solution to 5x^2+y^2-20x+19=0 is Ellipse with (h,k)=(2,0),a=sqrt(1/5),b=1