What is 3x^2+4y^2=48 ?

The solution to 3x^2+4y^2=48 is Ellipse with (h,k)=(0,0),a=4,b=2sqrt(3)

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3x^2+4y^2=48

3 x^{2} + 4 y^{2} = 48

(h, k) = (0, 0), a = 4, b = 23

Solution steps

3 x^{2} + 4 y^{2} = 48

Rewrite

3 x^{2} + 4 y^{2} = 48

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{4 ^{2}} + \frac{( y - 0 ) ^{2}}{( 2 3 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 4, b = 23

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 4, b = 23

9 (x - 3)^{2} + 4 (y - 4)^{2} = 36

\frac{( x - 7 ) ^{2}}{3} + \frac{( y + 11 ) ^{2}}{5} = 1

5 y (y + 4 x) + 4 x^{2} = - 20 (1 - x) y + 5

20 x^{2} + 4 y^{2} = 5

\frac{( x - 5 ) ^{2}}{12} + \frac{( y + 2 ) ^{2}}{16} = 1

What is 3x^2+4y^2=48 ?
The solution to 3x^2+4y^2=48 is Ellipse with (h,k)=(0,0),a=4,b=2sqrt(3)