What is 16x^2-96x+144+25y^2=400 ?

The solution to 16x^2-96x+144+25y^2=400 is Ellipse with (h,k)=(3,0),a=5,b=4

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16x^2-96x+144+25y^2=400

16 x^{2} - 96 x + 144 + 25 y^{2} = 400

(h, k) = (3, 0), a = 5, b = 4

Solution steps

16 x^{2} - 96 x + 144 + 25 y^{2} = 400

Rewrite

16 x^{2} - 96 x + 144 + 25 y^{2} = 400

in the form of the standard ellipse equation

\frac{( x - 3 ) ^{2}}{5 ^{2}} + \frac{( y - 0 ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (3, 0), a = 5, b = 4

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (3, 0), a = 5, b = 4

x^{2} = 20 y

x^{2} = 4 y

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

x^{2} - 6 x + y^{2} - 32 y = 0

(y - 2)^{2} = 8 (x - 1)

What is 16x^2-96x+144+25y^2=400 ?
The solution to 16x^2-96x+144+25y^2=400 is Ellipse with (h,k)=(3,0),a=5,b=4