What is 100x^2+4y^2=1 ?

The solution to 100x^2+4y^2=1 is Ellipse with (h,k)=(0,0),a= 1/10 ,b= 1/2

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100x^2+4y^2=1

100 x^{2} + 4 y^{2} = 1

(h, k) = (0, 0), a = \frac{1}{10}, b = \frac{1}{2}

Solution steps

100 x^{2} + 4 y^{2} = 1

Rewrite

100 x^{2} + 4 y^{2} = 1

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{1}{10} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{1}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{1}{10}, b = \frac{1}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = \frac{1}{2}, a = \frac{1}{10}

\frac{( x + 11 ) ^{2}}{100} + \frac{( y - 4 ) ^{2}}{1 9 ^{2}} = 1

4 x^{2} + 3 y^{2} + 4 x = 1

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

100 x^{2} + 9 y^{2} = 900

9 y^{2} + 16 x^{2} + 54 y - 64 x + 1 = 0

What is 100x^2+4y^2=1 ?
The solution to 100x^2+4y^2=1 is Ellipse with (h,k)=(0,0),a= 1/10 ,b= 1/2