What is 9y^2=144-16x^2 ?

The solution to 9y^2=144-16x^2 is Ellipse with (h,k)=(0,0),a=3,b=4

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9y^2=144-16x^2

9 y^{2} = 144 - 16 x^{2}

(h, k) = (0, 0), a = 3, b = 4

Solution steps

9 y^{2} = 144 - 16 x^{2}

Rewrite

9 y^{2} = 144 - 16 x^{2}

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{3 ^{2}} + \frac{( y - 0 ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 3, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 4, a = 3

x^{2} + 4 y^{2} + 10 x + 9 y - 7 = 0

16 x^{2} + 9 y^{2} - 32 x + 90 y + 145 = 0

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

\frac{( x - 2 ) ^{2}}{64} + \frac{( y - 4 ) ^{2}}{16} = 1

\frac{( x + 3 ) ^{2}}{4} + \frac{( y - 5 ) ^{2}}{25} = 1

What is 9y^2=144-16x^2 ?
The solution to 9y^2=144-16x^2 is Ellipse with (h,k)=(0,0),a=3,b=4