What is (1/4)x^2+y^2= 1/4 ?

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

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(1/4)x^2+y^2= 1/4

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

100 x^{2} + 4 y^{2} + 1200 x - 32 y + 3264 = 0

16 x^{2} + 15 y^{2} - 64 x - 90 y - 41 = 0

25 y^{2} + 9 x^{2} - 108 x - 200 y + 499 = 0

50 = \frac{100}{1 + x ^{2} + y ^{2}}

9 x^{2} + 4 y^{2} - 36 x + 8 y + 31 = 0

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