What is 36x^2+17y^2-648x+238y+689=0 ?

The solution to 36x^2+17y^2-648x+238y+689=0 is Ellipse with (h,k)=(9,-7),a=sqrt(85),b=6sqrt(5)

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36x^2+17y^2-648x+238y+689=0

36 x^{2} + 17 y^{2} - 648 x + 238 y + 689 = 0

(h, k) = (9, - 7), a = 85, b = 65

Solution steps

36 x^{2} + 17 y^{2} - 648 x + 238 y + 689 = 0

Rewrite

36 x^{2} + 17 y^{2} - 648 x + 238 y + 689 = 0

in the form of the standard ellipse equation

\frac{( x - 9 ) ^{2}}{( 85 ) ^{2}} + \frac{( y - ( - 7 ) ) ^{2}}{( 6 5 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (9, - 7), a = 85, b = 65

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (9, - 7), b = 65, a = 85

25 x^{2} + 16 y^{2} - 200 x - 160 y + 400 = 0

\frac{x ^{2}}{64} + \frac{( y - 6 ) ^{2}}{121} = 1

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

\frac{x ^{2}}{49} + \frac{y ^{2}}{40} = 1

3 = \frac{x ^{2}}{4} + \frac{y ^{2}}{9}

What is 36x^2+17y^2-648x+238y+689=0 ?
The solution to 36x^2+17y^2-648x+238y+689=0 is Ellipse with (h,k)=(9,-7),a=sqrt(85),b=6sqrt(5)