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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

2 x^{2} + 8 y^{2} = 50

\frac{( y - 1 ) ^{2}}{16} + \frac{( x + 3 ) ^{2}}{4} = 1

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

0.2 x^{2} + 2 y^{2} + 4 x - 8 y - 12 = 0

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

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