What is (x^2)/(4^2)+(y^2)/(5^2)=1 ?

The solution to (x^2)/(4^2)+(y^2)/(5^2)=1 is Ellipse with (h,k)=(0,0),a=4,b=5

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(x^2)/(4^2)+(y^2)/(5^2)=1

\frac{x ^{2}}{4 ^{2}} + \frac{y ^{2}}{5 ^{2}} = 1

(h, k) = (0, 0), a = 4, b = 5

Solution steps

\frac{x ^{2}}{4 ^{2}} + \frac{y ^{2}}{5 ^{2}} = 1

Rewrite

\frac{x ^{2}}{4 ^{2}} + \frac{y ^{2}}{5 ^{2}} = 1

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{4 ^{2}} + \frac{( y - 0 ) ^{2}}{5 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 4, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 5, a = 4

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\frac{x ^{2}}{64} + \frac{y ^{2}}{49} = 1

\frac{x ^{2}}{36} + \frac{y ^{2}}{100} = 1

4 x^{2} + 16 y^{2} - 8 x - 96 y + 84 = 0

x^{2} + 4 y^{2} - 10 x - 40 y + 109 = 0

What is (x^2)/(4^2)+(y^2)/(5^2)=1 ?
The solution to (x^2)/(4^2)+(y^2)/(5^2)=1 is Ellipse with (h,k)=(0,0),a=4,b=5