What is 81x^2+49y^2+486x-490y-2015=0 ?

The solution to 81x^2+49y^2+486x-490y-2015=0 is Ellipse with (h,k)=(-3,5),a=7,b=9

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81x^2+49y^2+486x-490y-2015=0

81 x^{2} + 49 y^{2} + 486 x - 490 y - 2015 = 0

(h, k) = (- 3, 5), a = 7, b = 9

Solution steps

81 x^{2} + 49 y^{2} + 486 x - 490 y - 2015 = 0

Rewrite

81 x^{2} + 49 y^{2} + 486 x - 490 y - 2015 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 3 ) ) ^{2}}{7 ^{2}} + \frac{( y - 5 ) ^{2}}{9 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 3, 5), a = 7, b = 9

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 3, 5), b = 9, a = 7

What is 81x^2+49y^2+486x-490y-2015=0 ?
The solution to 81x^2+49y^2+486x-490y-2015=0 is Ellipse with (h,k)=(-3,5),a=7,b=9