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

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

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x^2+4y^2=100

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

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

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

\frac{x ^{2}}{5 ^{2}} + \frac{y ^{2}}{7 ^{2}} = 1

9 x^{2} - 18 x + 4 y^{2} + 16 y - 11 = 0

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

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