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

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

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4x^2+3y^2=12

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

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

Solution steps

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

Rewrite

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

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

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

\frac{( x - 1 ) ^{2}}{45} + \frac{( y - 2 ) ^{2}}{20} = 1

4 x^{2} + 36 y^{2} - 24 x - 288 y + 611 = 0

\frac{x ^{2}}{8} + \frac{y ^{2}}{12} = 1

7 x^{2} + 2 y^{2} - 14 = 0

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