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

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

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

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

(h, k) = (0, 0), a = 3, b = 2

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 3 ) ^{2}} + \frac{( y - 0 ) ^{2}}{2 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 3, b = 2

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 2, a = 3

x^{2} + y^{2} = 6 y

\frac{( x + 2 ) ^{2}}{25} + \frac{( y - 1 ) ^{2}}{169} = 1

25 x^{2} + 4 y^{2} + 50 x - 16 y = 59

16 y^{2} + 25 x^{2} - 80 x + 36 y + 80 = 0

9 x^{2} + 4 y^{2} + 54 x - 8 y + 49 = 0

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