What is 8x^2+4y^2+16x-12y-15=0 ?

The solution to 8x^2+4y^2+16x-12y-15=0 is Ellipse with (h,k)=(-1, 3/2),a=2,b=2sqrt(2)

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8x^2+4y^2+16x-12y-15=0

8 x^{2} + 4 y^{2} + 16 x - 12 y - 15 = 0

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

Solution steps

8 x^{2} + 4 y^{2} + 16 x - 12 y - 15 = 0

Rewrite

8 x^{2} + 4 y^{2} + 16 x - 12 y - 15 = 0

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}}{81} + \frac{y ^{2}}{64} = 1

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

x^{2} + 10 x + 9 y^{2} + 16 = 0

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

\frac{x ^{2}}{7 ^{2}} + \frac{y ^{2}}{5 ^{2}} = 1

What is 8x^2+4y^2+16x-12y-15=0 ?
The solution to 8x^2+4y^2+16x-12y-15=0 is Ellipse with (h,k)=(-1, 3/2),a=2,b=2sqrt(2)