What is -25x^2-4y^2+100=4 ?

The solution to -25x^2-4y^2+100=4 is Ellipse with (h,k)=(0,0),a=(4sqrt(6))/5 ,b=2sqrt(6)

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-25x^2-4y^2+100=4

- 25 x^{2} - 4 y^{2} + 100 = 4

(h, k) = (0, 0), a = \frac{4 6}{5}, b = 26

Solution steps

- 25 x^{2} - 4 y^{2} + 100 = 4

Rewrite

- 25 x^{2} - 4 y^{2} + 100 = 4

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{4 6}{5} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 2 6 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{4 6}{5}, b = 26

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 26, a = \frac{4 6}{5}

\frac{( x - 6 ) ^{2}}{36} + \frac{( y + 2 ) ^{2}}{100} = 1

9 x^{2} - 72 x + 4 y^{2} + 40 y + 244 = 36

(x - a)^{2} + (y - (a - 16))^{2} = 1

3 x^{2} + 4 y^{2} + 6 x - 8 y - 5 = 0

27 x^{2} + 36 y^{2} + 108 x - 144 y - 720 = 0

What is -25x^2-4y^2+100=4 ?
The solution to -25x^2-4y^2+100=4 is Ellipse with (h,k)=(0,0),a=(4sqrt(6))/5 ,b=2sqrt(6)