What is 4x^2+3y^2+8x-6y-41=0 ?

The solution to 4x^2+3y^2+8x-6y-41=0 is Ellipse with (h,k)=(-1,1),a=2sqrt(3),b=4

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4x^2+3y^2+8x-6y-41=0

4 x^{2} + 3 y^{2} + 8 x - 6 y - 41 = 0

(h, k) = (- 1, 1), a = 23, b = 4

Solution steps

4 x^{2} + 3 y^{2} + 8 x - 6 y - 41 = 0

Rewrite

4 x^{2} + 3 y^{2} + 8 x - 6 y - 41 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 1, 1), a = 23, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 1, 1), b = 4, a = 23

x^{2} + 4 y^{2} + 4 y = 3

49 x^{2} + 16 y^{2} + 196 x - 96 y = 444

\frac{x ^{2}}{16} + \frac{( y - 2 ) ^{2}}{25} = 1

\frac{( x - 2 ) ^{2}}{16} + \frac{( y - 3 ) ^{2}}{25} = 1

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

What is 4x^2+3y^2+8x-6y-41=0 ?
The solution to 4x^2+3y^2+8x-6y-41=0 is Ellipse with (h,k)=(-1,1),a=2sqrt(3),b=4