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

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

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x^2+16y^2=1

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

9 x^{2} + 4 y^{2} - 36 x + 24 y + 36 = 0

25 x^{2} + 9 y^{2} - 150 x - 36 y = - 36

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

y = x^{2} + 2 y^{2} - 6

\frac{( x - 23 ) ^{2}}{841} + \frac{( y + 28 ) ^{2}}{484} = 1

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