What is 3x^2+7y^2=63 ?

The solution to 3x^2+7y^2=63 is Ellipse with (h,k)=(0,0),a=sqrt(21),b=3

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3x^2+7y^2=63

3 x^{2} + 7 y^{2} = 63

(h, k) = (0, 0), a = 21, b = 3

Solution steps

3 x^{2} + 7 y^{2} = 63

Rewrite

3 x^{2} + 7 y^{2} = 63

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 21 ) ^{2}} + \frac{( y - 0 ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 21, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 21, b = 3

4 x^{2} + 32 x + 9 y^{2} + 36 y + 64 = 0

\frac{x ^{2}}{9} + \frac{( y + 5 ) ^{2}}{25} = 1

\frac{( x - 2 ) ^{2}}{9} + \frac{( y + 3 ) ^{2}}{10} = 1

\frac{x ^{2}}{16} + \frac{y ^{2}}{64} = 1

4 x^{2} + 3 y^{2} - 5 x + 2 y + 1 = 0

What is 3x^2+7y^2=63 ?
The solution to 3x^2+7y^2=63 is Ellipse with (h,k)=(0,0),a=sqrt(21),b=3