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

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

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

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

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

Solution steps

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

Rewrite

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

4 x^{2} + 25 y^{2} - 100 = 0

16 x^{2} + 25 y^{2} = 100

64 x^{2} + 100 y^{2} + 768 x - 600 y - 3196 = 0

x^{2} + 4 y^{2} + 6 x - 8 y + 9 = 0

4 x^{2} + 9 y^{2} - 16 x + 54 y + 61 = 0

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