What is 3x^{(2)}+7y^{(2)}-12x-28y+19=0 ?

The solution to 3x^{(2)}+7y^{(2)}-12x-28y+19=0 is Ellipse with (h,k)=(2,2),a=sqrt(7),b=sqrt(3)

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3x^{(2)}+7y^{(2)}-12x-28y+19=0

3 x^{(2)} + 7 y^{(2)} - 12 x - 28 y + 19 = 0

(h, k) = (2, 2), a = 7, b = 3

Solution steps

3 x^{2} + 7 y^{2} - 12 x - 28 y + 19 = 0

Rewrite

3 x^{2} + 7 y^{2} - 12 x - 28 y + 19 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, 2), a = 7, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (2, 2), a = 7, b = 3

0 = x^{2} + y^{2} + 6 y

\frac{X ^{2}}{25} + \frac{Y ^{2}}{9} = 1

\frac{x ^{2}}{20} + \frac{y ^{2}}{36} = 1

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

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

What is 3x^{(2)}+7y^{(2)}-12x-28y+19=0 ?
The solution to 3x^{(2)}+7y^{(2)}-12x-28y+19=0 is Ellipse with (h,k)=(2,2),a=sqrt(7),b=sqrt(3)