What is 25x^{(2)}+4y^{(2)}=84 ?

The solution to 25x^{(2)}+4y^{(2)}=84 is Ellipse with (h,k)=(0,0),a=(2sqrt(21))/5 ,b=sqrt(21)

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25x^{(2)}+4y^{(2)}=84

25 x^{(2)} + 4 y^{(2)} = 84

(h, k) = (0, 0), a = \frac{2 21}{5}, b = 21

Solution steps

25 x^{2} + 4 y^{2} = 84

Rewrite

25 x^{2} + 4 y^{2} = 84

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{2 21}{5} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 21 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{2 21}{5}, b = 21

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 21, a = \frac{2 21}{5}

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

(x^{2} + 9 x + 4 y^{2} + 10 y) = 14

25 x^{2} + 9 y^{2} + 100 x - 54 y - 44 = 0

9 x^{2} + 4 y^{2} - 12 x = 0

2 x^{2} + 4 y^{2} = 8

What is 25x^{(2)}+4y^{(2)}=84 ?
The solution to 25x^{(2)}+4y^{(2)}=84 is Ellipse with (h,k)=(0,0),a=(2sqrt(21))/5 ,b=sqrt(21)