What is 13x^2+4y^2-52x-24y+36=0 ?

The solution to 13x^2+4y^2-52x-24y+36=0 is Ellipse with (h,k)=(2,3),a=2,b=sqrt(13)

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13x^2+4y^2-52x-24y+36=0

13 x^{2} + 4 y^{2} - 52 x - 24 y + 36 = 0

(h, k) = (2, 3), a = 2, b = 13

Solution steps

13 x^{2} + 4 y^{2} - 52 x - 24 y + 36 = 0

Rewrite

13 x^{2} + 4 y^{2} - 52 x - 24 y + 36 = 0

in the form of the standard ellipse equation

\frac{( x - 2 ) ^{2}}{2 ^{2}} + \frac{( y - 3 ) ^{2}}{( 13 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2, 3), a = 2, b = 13

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, 3), b = 13, a = 2

36 - 9 x^{2} - 4 y^{2} \geq 0

(x 3)^{2} + (y + 2)^{2} = 25

(\frac{( y - 8 )}{40})^{2} + (\frac{( x + 10 )}{211})^{2} = 1

1 = (\frac{x}{84.5})^{2} + (\frac{y}{33.5})^{2}

2 x^{2} + 3 y^{2} = 6

What is 13x^2+4y^2-52x-24y+36=0 ?
The solution to 13x^2+4y^2-52x-24y+36=0 is Ellipse with (h,k)=(2,3),a=2,b=sqrt(13)