What is 4x^2+8x+3y^2+6y-17=0 ?

The solution to 4x^2+8x+3y^2+6y-17=0 is Ellipse with (h,k)=(-1,-1),a=sqrt(6),b=2sqrt(2)

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4x^2+8x+3y^2+6y-17=0

4 x^{2} + 8 x + 3 y^{2} + 6 y - 17 = 0

(h, k) = (- 1, - 1), a = 6, b = 22

Solution steps

4 x^{2} + 8 x + 3 y^{2} + 6 y - 17 = 0

Rewrite

4 x^{2} + 8 x + 3 y^{2} + 6 y - 17 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 1, - 1), a = 6, b = 22

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 1, - 1), b = 22, a = 6

4 x^{2} + 16 y^{2} - 64 = 1

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

\frac{( x - 6 ) ^{2}}{36} + \frac{y ^{2}}{100} = 1

\frac{2 y}{x ^{2} + y ^{2}} < 1

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

What is 4x^2+8x+3y^2+6y-17=0 ?
The solution to 4x^2+8x+3y^2+6y-17=0 is Ellipse with (h,k)=(-1,-1),a=sqrt(6),b=2sqrt(2)