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

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

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4y^2+3x^2=48

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

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

Solution steps

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

Rewrite

4 y^{2} + 3 x^{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

4 (x - 1)^{2} + 9 (y - 1)^{2} = 36

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

\frac{x ^{2}}{20} + \frac{y ^{2}}{4} = 1

\frac{x ^{2}}{100} + \frac{y ^{2}}{16} = 1

4 x^{2} + 16 y^{2} - 16 x - 48 = 0

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