What is 110=x^2+3y^2 ?

The solution to 110=x^2+3y^2 is Ellipse with (h,k)=(0,0),a=sqrt(110),b=sqrt(110/3)

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110=x^2+3y^2

110 = x^{2} + 3 y^{2}

(h, k) = (0, 0), a = 110, b = \frac{110}{3}

Solution steps

110 = x^{2} + 3 y^{2}

Rewrite

110 = x^{2} + 3 y^{2}

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 110 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{110}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 110, b = \frac{110}{3}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 110, b = \frac{110}{3}

2 x^{2} + y^{2} + 4 x - 6 y = 7

\frac{( x - 8 ) ^{2}}{16} + \frac{( y + 1 ) ^{2}}{81} = 1

36 x^{2} + 9 y^{2} + 48 x - 36 y - 72 = 0

(x - 5)^{2} + (y - 1)^{2} + (y - 1)^{2} = 14

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

What is 110=x^2+3y^2 ?
The solution to 110=x^2+3y^2 is Ellipse with (h,k)=(0,0),a=sqrt(110),b=sqrt(110/3)