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

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

Popular >

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

X^{2} + 2 Y^{2} - 2 X - 4 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 Y^{2} - 2 X - 4 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}

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

4 x^{2} + 9 y^{2} - 8 x + 36 y - 104 = 0

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

4 X^{2} + 6 Y^{2} - 24 X + 2 Y - 12 = 0

25 y^{2} + 16 x^{2} + 50 y - 64 x - 311 = 0

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