What is 9x^2+25y^2-36x+50y-200=0 ?

The solution to 9x^2+25y^2-36x+50y-200=0 is Ellipse with (h,k)=(2,-1),a=sqrt(29),b=(3sqrt(29))/5

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9x^2+25y^2-36x+50y-200=0

9 x^{2} + 25 y^{2} - 36 x + 50 y - 200 = 0

(h, k) = (2, - 1), a = 29, b = \frac{3 29}{5}

Solution steps

9 x^{2} + 25 y^{2} - 36 x + 50 y - 200 = 0

Rewrite

9 x^{2} + 25 y^{2} - 36 x + 50 y - 200 = 0

in the form of the standard ellipse equation

\frac{( x - 2 ) ^{2}}{( 29 ) ^{2}} + \frac{( y - ( - 1 ) ) ^{2}}{( \frac{3 29}{5} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2, - 1), a = 29, b = \frac{3 29}{5}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (2, - 1), a = 29, b = \frac{3 29}{5}

\frac{( X + 2 ) ^{2}}{4} + \frac{( y - 3 ) ^{2}}{9} = 1

7 x^{2} + 16 y^{2} - 112 = 0

(x - h)^{2} + (y - k)^{2} = 1

9 x^{2} + 64 y^{2} = 1

\frac{( x - 2 ) ^{2}}{9} + \frac{( y + 1 ) ^{2}}{25} = 1

What is 9x^2+25y^2-36x+50y-200=0 ?
The solution to 9x^2+25y^2-36x+50y-200=0 is Ellipse with (h,k)=(2,-1),a=sqrt(29),b=(3sqrt(29))/5