What is 4x^2+24y^2=100 ?

The solution to 4x^2+24y^2=100 is Ellipse with (h,k)=(0,0),a=5,b= 5/(sqrt(6))

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4x^2+24y^2=100

4 x^{2} + 24 y^{2} = 100

(h, k) = (0, 0), a = 5, b = \frac{5}{6}

Solution steps

4 x^{2} + 24 y^{2} = 100

Rewrite

4 x^{2} + 24 y^{2} = 100

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{5 ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{5}{6} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 5, b = \frac{5}{6}

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}{6}

- x^{2} - 2 y^{2} = - 40

9 x^{2} + 16 y^{2} - 36 x - 64 y + (- 44) = 0

(\frac{x - 4}{6})^{2} + (\frac{y + 2}{6})^{2} = 1

4 x^{2} + 9 y^{2} = 11

\frac{( x - 4 ) ^{2}}{9} + \frac{( y + 2 ) ^{2}}{4} = 1

What is 4x^2+24y^2=100 ?
The solution to 4x^2+24y^2=100 is Ellipse with (h,k)=(0,0),a=5,b= 5/(sqrt(6))