What is (x^2}{85}+\frac{y^2)/4 =1 ?

The solution to (x^2}{85}+\frac{y^2)/4 =1 is Ellipse with (h,k)=(0,0),a=sqrt(85),b=2

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(x^2}{85}+\frac{y^2)/4 =1

\frac{x ^{2}}{85} + \frac{y ^{2}}{4} = 1

(h, k) = (0, 0), a = 85, b = 2

Solution steps

\frac{x ^{2}}{85} + \frac{y ^{2}}{4} = 1

Rewrite

\frac{x ^{2}}{85} + \frac{y ^{2}}{4} = 1

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 85 ) ^{2}} + \frac{( y - 0 ) ^{2}}{2 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 85, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 85, b = 2

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X^{2} + 2 Y^{2} - 2 X - 4 Y - 8 = 0

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

4 x^{2} + 9 y^{2} - 8 x + 36 y - 104 = 0

What is (x^2}{85}+\frac{y^2)/4 =1 ?
The solution to (x^2}{85}+\frac{y^2)/4 =1 is Ellipse with (h,k)=(0,0),a=sqrt(85),b=2