What is 4y^{(2)}+2x^{(2)}-4y-8x-15=0 ?

The solution to 4y^{(2)}+2x^{(2)}-4y-8x-15=0 is Ellipse with (h,k)=(2, 1/2),a=2sqrt(3),b=sqrt(6)

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4y^{(2)}+2x^{(2)}-4y-8x-15=0

4 y^{(2)} + 2 x^{(2)} - 4 y - 8 x - 15 = 0

(h, k) = (2, \frac{1}{2}), a = 23, b = 6

Solution steps

4 y^{2} + 2 x^{2} - 4 y - 8 x - 15 = 0

Rewrite

4 y^{2} + 2 x^{2} - 4 y - 8 x - 15 = 0

in the form of the standard ellipse equation

\frac{( x - 2 ) ^{2}}{( 2 3 ) ^{2}} + \frac{( y - \frac{1}{2} ) ^{2}}{( 6 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2, \frac{1}{2}), a = 23, b = 6

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (2, \frac{1}{2}), a = 23, b = 6

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

\frac{x ^{2}}{1} + \frac{y ^{2}}{a - 16} = 1

9 x^{2} + 5 y^{2} - 18 x - 40 y + 44 = 0

\frac{( x - 3 ) ^{2}}{9} + \frac{( y - 4 ) ^{2}}{16} = 1

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

What is 4y^{(2)}+2x^{(2)}-4y-8x-15=0 ?
The solution to 4y^{(2)}+2x^{(2)}-4y-8x-15=0 is Ellipse with (h,k)=(2, 1/2),a=2sqrt(3),b=sqrt(6)