What is 5x^2+6y^2+70x+84y+509=0 ?

The solution to 5x^2+6y^2+70x+84y+509=0 is Ellipse with (h,k)=(-7,-7),a=sqrt(6),b=sqrt(5)

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5x^2+6y^2+70x+84y+509=0

5 x^{2} + 6 y^{2} + 70 x + 84 y + 509 = 0

(h, k) = (- 7, - 7), a = 6, b = 5

Solution steps

5 x^{2} + 6 y^{2} + 70 x + 84 y + 509 = 0

Rewrite

5 x^{2} + 6 y^{2} + 70 x + 84 y + 509 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 7 ) ) ^{2}}{( 6 ) ^{2}} + \frac{( y - ( - 7 ) ) ^{2}}{( 5 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 7, - 7), a = 6, b = 5

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 7, - 7), a = 6, b = 5

2 x^{2} + 4 y^{2} - 8 = 0

9 (x - 1)^{2} + 4 (y + 2)^{2} = 36

3 x^{2} + 5 y + 5 y^{2} = 5

\frac{( x - 6 ) ^{2}}{36} + \frac{( y + 4 ) ^{2}}{16} = 1

49 x^{2} + 9 y^{2} = 16

What is 5x^2+6y^2+70x+84y+509=0 ?
The solution to 5x^2+6y^2+70x+84y+509=0 is Ellipse with (h,k)=(-7,-7),a=sqrt(6),b=sqrt(5)