What is 16x^2+25y^2-32x-150y-159=0 ?

The solution to 16x^2+25y^2-32x-150y-159=0 is Ellipse with (h,k)=(1,3),a=5,b=4

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16x^2+25y^2-32x-150y-159=0

16 x^{2} + 25 y^{2} - 32 x - 150 y - 159 = 0

(h, k) = (1, 3), a = 5, b = 4

Solution steps

16 x^{2} + 25 y^{2} - 32 x - 150 y - 159 = 0

Rewrite

16 x^{2} + 25 y^{2} - 32 x - 150 y - 159 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, 3), a = 5, b = 4

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, 3), a = 5, b = 4

\frac{( y - 2 ) ^{2}}{9} + \frac{( \frac{x + 1}{2} ) ^{2}}{9} = 1

\frac{( x - 2 ) ^{2}}{9} + \frac{( y - 1 ) ^{2}}{4} = 1

x^{2} + y^{2} = 9 y

\frac{x ^{2}}{36} + \frac{y ^{2}}{2. 5 ^{2}} = 1

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

What is 16x^2+25y^2-32x-150y-159=0 ?
The solution to 16x^2+25y^2-32x-150y-159=0 is Ellipse with (h,k)=(1,3),a=5,b=4