What is X^2+2*Y^2-2*X-4*Y-8=0 ?

The solution to X^2+2*Y^2-2*X-4*Y-8=0 is Ellipse with (h,k)=(1,1),a=sqrt(11),b=sqrt(11/2)

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X^2+2Y^2-2X-4*Y-8=0

X^{2} + 2 \cdot Y^{2} - 2 \cdot X - 4 \cdot Y - 8 = 0

(h, k) = (1, 1), a = 11, b = \frac{11}{2}

Solution steps

X^{2} + 2 Y^{2} - 2 X - 4 Y - 8 = 0

Rewrite

X^{2} + 2 \cdot Y^{2} - 2 \cdot X - 4 \cdot Y - 8 = 0

in the form of the standard ellipse equation

\frac{( X - 1 ) ^{2}}{( 11 ) ^{2}} + \frac{( Y - 1 ) ^{2}}{( \frac{11}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (1, 1), a = 11, b = \frac{11}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, 1), a = 11, b = \frac{11}{2}

\frac{x ^{2}}{21} + \frac{y ^{2}}{25} = 1

4 x^{2} + 16 y^{2} + 16 x + 160 y + 352 = 0

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

\frac{( x + 9 ) ^{2}}{81} + \frac{( y - 1 ) ^{2}}{9} = 1

9 x^{2} + 25 y^{2} - 36 x + 50 y - 200 = 0

What is X^2+2*Y^2-2*X-4*Y-8=0 ?
The solution to X^2+2*Y^2-2*X-4*Y-8=0 is Ellipse with (h,k)=(1,1),a=sqrt(11),b=sqrt(11/2)