What is -4x^2-7y^2>-28 ?

The solution to -4x^2-7y^2>-28 is Ellipse with (h,k)=(0,0),a=sqrt(7),b=2

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-4x^2-7y^2>-28

- 4 x^{2} - 7 y^{2} > - 28

(h, k) = (0, 0), a = 7, b = 2

Solution steps

- 4 x^{2} - 7 y^{2} > - 28

Rewrite

- 4 x^{2} - 7 y^{2} > - 28

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 7 ) ^{2}} + \frac{( y - 0 ) ^{2}}{2 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 7, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 7, b = 2

\frac{1}{4} (x - 2)^{2} + \frac{1}{16} (y + 7)^{2} = 1

4 = x^{2} + 9 y^{2}

1 x^{2} + 3 y^{2} + 9 x + 9 y - 12 = 0

\frac{y ^{2}}{4} + \frac{x ^{2}}{16} = 1

9 x^{2} + 4 y^{2} + 8 x + 48 y = - 117

What is -4x^2-7y^2>-28 ?
The solution to -4x^2-7y^2>-28 is Ellipse with (h,k)=(0,0),a=sqrt(7),b=2