What is 7x^2+3y^2=55 ?

The solution to 7x^2+3y^2=55 is Ellipse with (h,k)=(0,0),a=sqrt(55/7),b=sqrt(55/3)

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7x^2+3y^2=55

7 x^{2} + 3 y^{2} = 55

(h, k) = (0, 0), a = \frac{55}{7}, b = \frac{55}{3}

Solution steps

7 x^{2} + 3 y^{2} = 55

Rewrite

7 x^{2} + 3 y^{2} = 55

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{55}{7} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{55}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{55}{7}, b = \frac{55}{3}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = \frac{55}{3}, a = \frac{55}{7}

\frac{( x - 2 ) ^{2}}{6} + \frac{( y - 6 2 ) ^{2}}{8} = 1

\frac{x ^{2}}{81} + \frac{y ^{2}}{121} = 1

x^{2} + 64 x + 9 y^{2} + 162 y + 949 = 0

3 x^{2} + 2 y^{2} - 6 x + 8 y + 5 = 0

\frac{( x + 3 ) ^{2}}{21} + \frac{( y - 6 ) ^{2}}{25} = 1

What is 7x^2+3y^2=55 ?
The solution to 7x^2+3y^2=55 is Ellipse with (h,k)=(0,0),a=sqrt(55/7),b=sqrt(55/3)