What is x^2+4y^2-46=0 ?

The solution to x^2+4y^2-46=0 is Ellipse with (h,k)=(0,0),a=sqrt(46),b=sqrt(23/2)

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x^2+4y^2-46=0

x^{2} + 4 y^{2} - 46 = 0

(h, k) = (0, 0), a = 46, b = \frac{23}{2}

Solution steps

x^{2} + 4 y^{2} - 46 = 0

Rewrite

x^{2} + 4 y^{2} - 46 = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 46 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{23}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 46, b = \frac{23}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 46, b = \frac{23}{2}

\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} - 1 = 0

x^{2} + 2 x + 3 y^{2} = 6

\frac{x ^{2}}{9} + \frac{y ^{2}}{81} = 1

- 4 x^{2} - y^{2} + 14 x - 5 y - 45 = 0

\frac{( x + 1 ) ^{2}}{20} + \frac{( y - 1 ) ^{2}}{36} = 1

What is x^2+4y^2-46=0 ?
The solution to x^2+4y^2-46=0 is Ellipse with (h,k)=(0,0),a=sqrt(46),b=sqrt(23/2)