What is 8x^2+16x+4y^2-12y=15 ?

The solution to 8x^2+16x+4y^2-12y=15 is Ellipse with (h,k)=(-1, 3/2),a=2,b=2sqrt(2)

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8x^2+16x+4y^2-12y=15

8 x^{2} + 16 x + 4 y^{2} - 12 y = 15

(h, k) = (- 1, \frac{3}{2}), a = 2, b = 22

Solution steps

8 x^{2} + 16 x + 4 y^{2} - 12 y = 15

Rewrite

8 x^{2} + 16 x + 4 y^{2} - 12 y = 15

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 1, \frac{3}{2}), a = 2, b = 22

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 1, \frac{3}{2}), b = 22, a = 2

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

\frac{x ^{2}}{400} + \frac{y ^{2}}{256} = 1

3 x^{2} + y^{2} - 25 = 0

3 x^{2} + 12 y^{2} + 6 x - 24 y + 6 = 0

x^{2} + 4 y^{2} + 2 x - 16 y + 13 = 0

What is 8x^2+16x+4y^2-12y=15 ?
The solution to 8x^2+16x+4y^2-12y=15 is Ellipse with (h,k)=(-1, 3/2),a=2,b=2sqrt(2)