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

The solution to y^2=100-4x^2 is Ellipse with (h,k)=(0,0),a=5,b=10

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y^2=100-4x^2

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

(h, k) = (0, 0), a = 5, b = 10

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 5, b = 10

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 10, a = 5

4 x^{2} + y^{2} + 4 x + 8 y + 12 = 0

\frac{( x - 3 ) ^{2}}{18} + \frac{( y + 4 ) ^{2}}{32} = 1

\frac{( y - 4 ) ^{2}}{9} + \frac{( x - 1 ) ^{2}}{4} = 1

\frac{x ^{2}}{85} + \frac{y ^{2}}{4} = 1

x, \frac{x ^{2}}{16} + \frac{Y ( x ) ^{2}}{4} = 1

What is y^2=100-4x^2 ?
The solution to y^2=100-4x^2 is Ellipse with (h,k)=(0,0),a=5,b=10