What is ((x^2))/((16))+((y^2))/((12))=1 ?

The solution to ((x^2))/((16))+((y^2))/((12))=1 is Ellipse with (h,k)=(0,0),a=4,b=2sqrt(3)

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((x^2))/((16))+((y^2))/((12))=1

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

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

Solution steps

\frac{x ^{2}}{16} + \frac{y ^{2}}{12} = 1

Rewrite

\frac{x ^{2}}{16} + \frac{y ^{2}}{12} = 1

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

\frac{( x - 3 ) ^{2}}{16} + \frac{( y - 7 ) ^{2}}{64} = 1

2 x^{2} + 3 y^{2} + 4 x = 19

x^{2} + 6 x + (5 y + 6)^{2} - 2 (5 y + 6) + 10 = 4

25 y^{2} + 36 (x - 8)^{2} = 900

x^{2} + 3 y^{2} - 4 x + 12 y + 13 = 0

What is ((x^2))/((16))+((y^2))/((12))=1 ?
The solution to ((x^2))/((16))+((y^2))/((12))=1 is Ellipse with (h,k)=(0,0),a=4,b=2sqrt(3)