What is -8y^2+72<9x^2 ?

The solution to -8y^2+72<9x^2 is Ellipse with (h,k)=(0,0),a=2sqrt(2),b=3

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-8y^2+72<9x^2

- 8 y^{2} + 72 < 9 x^{2}

(h, k) = (0, 0), a = 22, b = 3

Solution steps

- 8 y^{2} + 72 < 9 x^{2}

Rewrite

- 8 y^{2} + 72 < 9 x^{2}

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 22, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 3, a = 22

4 x^{2} + 9 y^{2} + 16 x + 54 y + 61 = 0

4 x^{2} - 16 x + y^{2} + 2 y + 13 = 0

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

3 x^{2} + 2 y^{2} - 16 x + 15 = 0

\frac{x ^{2}}{400} + \frac{y ^{2}}{100} = 1

What is -8y^2+72<9x^2 ?
The solution to -8y^2+72<9x^2 is Ellipse with (h,k)=(0,0),a=2sqrt(2),b=3