What is 42x^2+49y^2=4 ?

The solution to 42x^2+49y^2=4 is Ellipse with (h,k)=(0,0),a=sqrt(2/21),b= 2/7

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42x^2+49y^2=4

42 x^{2} + 49 y^{2} = 4

(h, k) = (0, 0), a = \frac{2}{21}, b = \frac{2}{7}

Solution steps

42 x^{2} + 49 y^{2} = 4

Rewrite

42 x^{2} + 49 y^{2} = 4

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{2}{21} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{2}{7} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{2}{21}, b = \frac{2}{7}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = \frac{2}{21}, b = \frac{2}{7}

\frac{x ^{2}}{C 1 ^{2}} = 1 - \frac{y ^{2}}{C 2 ^{2}}

\frac{( x - 1 ) ^{2}}{169} + \frac{( y - 4 ) ^{2}}{144} = 1

9 x^{2} + 25 y^{2} - 18 x - 50 y - 191 = 0

3 x^{2} + 3 y^{2} - 6 y = 0

\frac{( x - 3 ) ^{2}}{4} + \frac{( y + 1 ) ^{2}}{25} = 1

What is 42x^2+49y^2=4 ?
The solution to 42x^2+49y^2=4 is Ellipse with (h,k)=(0,0),a=sqrt(2/21),b= 2/7