What is 8x^2+16y^2=1 ?

The solution to 8x^2+16y^2=1 is Ellipse with (h,k)=(0,0),a= 1/(2sqrt(2)),b= 1/4

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8x^2+16y^2=1

8 x^{2} + 16 y^{2} = 1

(h, k) = (0, 0), a = \frac{1}{2 2}, b = \frac{1}{4}

Solution steps

8 x^{2} + 16 y^{2} = 1

Rewrite

8 x^{2} + 16 y^{2} = 1

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{1}{2 2} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{1}{4} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{1}{2 2}, b = \frac{1}{4}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = \frac{1}{2 2}, b = \frac{1}{4}

\frac{( x - 8 ) ^{2}}{4} + \frac{( y - 4 ) ^{2}}{1} = 1

4 x^{2} + 9 y^{2} \leq 36

x^{2} + 6 x + 9 + y^{2} = 28.09 + \frac{9 x ^{2}}{16}

\frac{( x + 2 ) ^{2}}{36} + \frac{( y - 3 ) ^{2}}{9} = 1

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

What is 8x^2+16y^2=1 ?
The solution to 8x^2+16y^2=1 is Ellipse with (h,k)=(0,0),a= 1/(2sqrt(2)),b= 1/4