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

2 = 4 x^{2} + y^{2} + 1

9 x^{2} + 16 y^{2} + 54 x - 32 y - 47 = 0

16 x^{2} + 25 y^{2} - 32 x - 150 y - 159 = 0

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

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