What is 3x^2+2y^2<= 13950 ?

The solution to 3x^2+2y^2<= 13950 is Ellipse with (h,k)=(0,0),a=5sqrt(186),b=15sqrt(31)

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3x^2+2y^2<= 13950

3 x^{2} + 2 y^{2} \leq 13950

(h, k) = (0, 0), a = 5186, b = 1531

Solution steps

3 x^{2} + 2 y^{2} \leq 13950

Rewrite

3 x^{2} + 2 y^{2} \leq 13950

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 5 186 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 15 31 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 5186, b = 1531

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 1531, a = 5186

\frac{( x - 3 ) ^{2}}{16} + \frac{( y + 1 ) ^{2}}{9} = 1

\frac{( x + 1 ) ^{2}}{4} + \frac{( y + 1 ) ^{2}}{9} = 1

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

\frac{( x ) ^{2}}{25} + \frac{( y ) ^{2}}{16} = 1

\frac{x ^{2}}{256} + \frac{y ^{2}}{400} = 2

What is 3x^2+2y^2<= 13950 ?
The solution to 3x^2+2y^2<= 13950 is Ellipse with (h,k)=(0,0),a=5sqrt(186),b=15sqrt(31)