What is 4x^2+3y^2-8x+12y-32=0 ?

The solution to 4x^2+3y^2-8x+12y-32=0 is Ellipse with (h,k)=(1,-2),a=2sqrt(3),b=4

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4x^2+3y^2-8x+12y-32=0

4 x^{2} + 3 y^{2} - 8 x + 12 y - 32 = 0

(h, k) = (1, - 2), a = 23, b = 4

Solution steps

4 x^{2} + 3 y^{2} - 8 x + 12 y - 32 = 0

Rewrite

4 x^{2} + 3 y^{2} - 8 x + 12 y - 32 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, - 2), a = 23, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, - 2), b = 4, a = 23

x^{2} + 4 y^{2} - 6 x - 55 = 0

9 x^{2} + 4 y^{2} + 36 x + 16 y + 16 = 0

(\frac{x - 2}{4})^{2} + (\frac{y + 3}{16})^{2} = 1

\frac{( x - 2 ) ^{2}}{25} + \frac{( y + 3 ) ^{2}}{4} = 1

\frac{x ^{2}}{25} + \frac{y ^{2}}{\frac{25}{4}} = 1

What is 4x^2+3y^2-8x+12y-32=0 ?
The solution to 4x^2+3y^2-8x+12y-32=0 is Ellipse with (h,k)=(1,-2),a=2sqrt(3),b=4