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

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

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25x^2+4y^2=100

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

(h, k) = (0, 0), a = 2, b = 5

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 2, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 5, a = 2

y = - 2 x^{2} - 2 x - 2

\frac{x ^{2}}{9} + \frac{y ^{2}}{16} = 1

x^{2} - y^{2} = 25

x^{2} + y^{2} = 100

y^{2} = - 14 x

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