What is X^2+8Y^2-5=0 ?

The solution to X^2+8Y^2-5=0 is Ellipse with (h,k)=(0,0),a=sqrt(5),b=(sqrt(5))/(2sqrt(2))

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X^2+8Y^2-5=0

X^{2} + 8 Y^{2} - 5 = 0

(h, k) = (0, 0), a = 5, b = \frac{5}{2 2}

Solution steps

X^{2} + 8 Y^{2} - 5 = 0

Rewrite

X^{2} + 8 Y^{2} - 5 = 0

in the form of the standard ellipse equation

\frac{( X - 0 ) ^{2}}{( 5 ) ^{2}} + \frac{( Y - 0 ) ^{2}}{( \frac{5}{2 2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 5, b = \frac{5}{2 2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 5, b = \frac{5}{2 2}

\frac{( x - 2 ) ^{2}}{12} + \frac{( y + 5 ) ^{2}}{8} = 1

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

4 (x - 3)^{2} + 2 y^{2} = 8

9 x^{2} + 36 y^{2} + 18 x - 360 y + 585 = 0

\frac{x ^{2}}{49} + \frac{y ^{2}}{24} = 1

What is X^2+8Y^2-5=0 ?
The solution to X^2+8Y^2-5=0 is Ellipse with (h,k)=(0,0),a=sqrt(5),b=(sqrt(5))/(2sqrt(2))