What is x^2-10x+4y^2-8y=5 ?

The solution to x^2-10x+4y^2-8y=5 is Ellipse with (h,k)=(5,1),a=sqrt(34),b=sqrt(17/2)

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x^2-10x+4y^2-8y=5

x^{2} - 10 x + 4 y^{2} - 8 y = 5

(h, k) = (5, 1), a = 34, b = \frac{17}{2}

Solution steps

x^{2} - 10 x + 4 y^{2} - 8 y = 5

Rewrite

x^{2} - 10 x + 4 y^{2} - 8 y = 5

in the form of the standard ellipse equation

\frac{( x - 5 ) ^{2}}{( 34 ) ^{2}} + \frac{( y - 1 ) ^{2}}{( \frac{17}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (5, 1), a = 34, b = \frac{17}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (5, 1), a = 34, b = \frac{17}{2}

\frac{( x + 3 ) ^{2}}{9} + \frac{( y - 2 ) ^{2}}{5} = 1

\frac{x ^{2}}{2} + \frac{y ^{2}}{3} = 1

9 x^{2} + y^{2} + 18 x + 2 y + 1 = 0

2 x^{2} + 8 y^{2} = 25

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

What is x^2-10x+4y^2-8y=5 ?
The solution to x^2-10x+4y^2-8y=5 is Ellipse with (h,k)=(5,1),a=sqrt(34),b=sqrt(17/2)