What is 9x^2+49y^2+18x+294y-9=0 ?

The solution to 9x^2+49y^2+18x+294y-9=0 is Ellipse with (h,k)=(-1,-3),a=sqrt(51),b=(3sqrt(51))/7

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9x^2+49y^2+18x+294y-9=0

9 x^{2} + 49 y^{2} + 18 x + 294 y - 9 = 0

(h, k) = (- 1, - 3), a = 51, b = \frac{3 51}{7}

Solution steps

9 x^{2} + 49 y^{2} + 18 x + 294 y - 9 = 0

Rewrite

9 x^{2} + 49 y^{2} + 18 x + 294 y - 9 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 1 ) ) ^{2}}{( 51 ) ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{( \frac{3 51}{7} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 1, - 3), a = 51, b = \frac{3 51}{7}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 1, - 3), a = 51, b = \frac{3 51}{7}

\frac{x ^{2}}{4 ^{2}} + \frac{y ^{2}}{7 ^{2}} = 1

3 = x^{2} + 4 y^{2}

\frac{X ^{2}}{4} + \frac{Y ^{2}}{9} = 4

\frac{x ^{2}}{2.4 8 ^{2}} + \frac{y ^{2}}{2.7 5 ^{2}} = 1

x^{2} + 4 y^{2} - 16 y - 1 = - 1

What is 9x^2+49y^2+18x+294y-9=0 ?
The solution to 9x^2+49y^2+18x+294y-9=0 is Ellipse with (h,k)=(-1,-3),a=sqrt(51),b=(3sqrt(51))/7