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

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

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4x^2+25y^2=100

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

x^{2} = 4 y

x^{2} = - 16 y

y - x > - x^{2} - 1

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

x = \frac{1}{8} y^{2}

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