What is ((x^2)/a)+((y^2)/b)=1 ?

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

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((x^2)/a)+((y^2)/b)=1

(\frac{x ^{2}}{a}) + (\frac{y ^{2}}{b}) = 1

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

\frac{( x - 10 ) ^{2}}{25} + \frac{( y - 4 ) ^{2}}{36} = 1

3 x^{2} + 2 y^{2} - 6 x + 4 y - 2 = 0

9 x^{(2)} + 25 y^{(2)} + 18 x + 150 y + 9 = 0

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

9 x^{2} + 25 y^{2} + 36 x - 200 y + 211 = 0

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