x^2+3y^2=7

Solution

x^{2} + 3 y^{2} = 7

(h, k) = (0, 0), a = 7, b = \frac{7}{3}

Solution steps

x^{2} + 3 y^{2} = 7

Rewrite

x^{2} + 3 y^{2} = 7

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 7 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{7}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 7, b = \frac{7}{3}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 7, b = \frac{7}{3}

\frac{( x - 8 ) ^{2}}{49} + \frac{( y + 5 ) ^{2}}{9} = 1

\frac{( x - 42 ) ^{2}}{12} + \frac{( y - 20 ) ^{2}}{27} = 1

16 x^{2} + 25 (y + 3)^{2} = 1600

\frac{( x - ( - 1.32 ) ) ^{2}}{3.78} + \frac{y ^{2}}{1.56} = 2

\frac{x ^{2}}{16} - \frac{x}{8} + 9 y^{2} - 18 y + \frac{17}{2} = 0

What is x^2+3y^2=7 ?
The solution to x^2+3y^2=7 is Ellipse with (h,k)=(0,0),a=sqrt(7),b=sqrt(7/3)