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

The solution to 8x^2+2y^2+16x=1 is Ellipse with (h,k)=(-1,0),a= 3/(2sqrt(2)),b= 3/(sqrt(2))

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

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

(h, k) = (- 1, 0), a = \frac{3}{2 2}, b = \frac{3}{2}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - ( - 1 ) ) ^{2}}{( \frac{3}{2 2} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{3}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 1, 0), a = \frac{3}{2 2}, b = \frac{3}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 1, 0), b = \frac{3}{2}, a = \frac{3}{2 2}

x^{2} + 6 y^{2} + 14 x - 24 y + 49 = 0

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

- y^{2} - x^{2} = 1

\frac{1}{9} x^{2} + \frac{1}{16} y^{2} = 1

4 (x - 2)^{2} + 9 (y - 3)^{2} = 36

What is 8x^2+2y^2+16x=1 ?
The solution to 8x^2+2y^2+16x=1 is Ellipse with (h,k)=(-1,0),a= 3/(2sqrt(2)),b= 3/(sqrt(2))