What is x^2+6y^2+14x-24y+49=0 ?

The solution to x^2+6y^2+14x-24y+49=0 is Ellipse with (h,k)=(-7,2),a=2sqrt(6),b=2

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x^2+6y^2+14x-24y+49=0

x^{2} + 6 y^{2} + 14 x - 24 y + 49 = 0

(h, k) = (- 7, 2), a = 26, b = 2

Solution steps

x^{2} + 6 y^{2} + 14 x - 24 y + 49 = 0

Rewrite

x^{2} + 6 y^{2} + 14 x - 24 y + 49 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 7 ) ) ^{2}}{( 2 6 ) ^{2}} + \frac{( y - 2 ) ^{2}}{2 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 7, 2), a = 26, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 7, 2), a = 26, b = 2

4 x^{2} + 9 y^{2} + 16 x - 18 y - 11 = 0

- y^{2} - x^{2} = 1

\frac{1}{9} x^{2} + \frac{1}{16} y^{2} = 1

4 (x - 2)^{2} + 9 (y - 3)^{2} = 36

\frac{x ^{2}}{7. 5 ^{2}} + \frac{y ^{2}}{9 ^{2}} = 1

What is x^2+6y^2+14x-24y+49=0 ?
The solution to x^2+6y^2+14x-24y+49=0 is Ellipse with (h,k)=(-7,2),a=2sqrt(6),b=2