What is 9x^2+26y^2=60 ?

The solution to 9x^2+26y^2=60 is Ellipse with (h,k)=(0,0),a=(2sqrt(5))/(sqrt(3)),b=sqrt(30/13)

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9x^2+26y^2=60

9 x^{2} + 26 y^{2} = 60

(h, k) = (0, 0), a = \frac{2 5}{3}, b = \frac{30}{13}

Solution steps

9 x^{2} + 26 y^{2} = 60

Rewrite

9 x^{2} + 26 y^{2} = 60

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{2 5}{3} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{30}{13} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{2 5}{3}, b = \frac{30}{13}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = \frac{2 5}{3}, b = \frac{30}{13}

8 x^{2} + 9 y^{2} - 16 x - 54 y + 17 = 0

x^{2} + 3 y^{2} = 112

\frac{( y + 16 ) ^{2}}{400} + \frac{x ^{2}}{144} = 1

\frac{( x + 3 ) ^{2}}{21} + \frac{( y - 2 ) ^{2}}{49} = 1

16 - x^{2} - 9 y^{2} \geq 0

What is 9x^2+26y^2=60 ?
The solution to 9x^2+26y^2=60 is Ellipse with (h,k)=(0,0),a=(2sqrt(5))/(sqrt(3)),b=sqrt(30/13)