What is (x^2)/4+(y^2)/(84)=1 ?

The solution to (x^2)/4+(y^2)/(84)=1 is Ellipse with (h,k)=(0,0),a=2,b=2sqrt(21)

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(x^2)/4+(y^2)/(84)=1

\frac{x ^{2}}{4} + \frac{y ^{2}}{84} = 1

(h, k) = (0, 0), a = 2, b = 221

Solution steps

\frac{x ^{2}}{4} + \frac{y ^{2}}{84} = 1

Rewrite

\frac{x ^{2}}{4} + \frac{y ^{2}}{84} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 2, b = 221

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 221, a = 2

25 x^{2} + 9 y^{2} - 100 x + 18 y - 118 = 0

\frac{( x - 5 ) ^{2}}{64} + \frac{y ^{2}}{89} = 1

2 x^{2} + 6 y^{2} = 12

5 x^{2} + 9 y^{2} - 45 = 0

2 (x^{2} + y^{2}) = x^{2} + (y - \frac{5}{2})^{2} - \frac{25}{4}

What is (x^2)/4+(y^2)/(84)=1 ?
The solution to (x^2)/4+(y^2)/(84)=1 is Ellipse with (h,k)=(0,0),a=2,b=2sqrt(21)