What is 16x^2+25y^2-32x-100y-284=0 ?

The solution to 16x^2+25y^2-32x-100y-284=0 is Ellipse with (h,k)=(1,2),a=5,b=4

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16x^2+25y^2-32x-100y-284=0

16 x^{2} + 25 y^{2} - 32 x - 100 y - 284 = 0

(h, k) = (1, 2), a = 5, b = 4

Solution steps

16 x^{2} + 25 y^{2} - 32 x - 100 y - 284 = 0

Rewrite

16 x^{2} + 25 y^{2} - 32 x - 100 y - 284 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, 2), a = 5, b = 4

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, 2), a = 5, b = 4

9 x^{2} - 54 x + 4 y^{2} - 8 y - 59 = 0

\frac{( x + 5 ) ^{2}}{20} + \frac{( y - 6 ) ^{2}}{11} = 1

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

x^{2} + y^{2} + y^{2} = \frac{9}{4}

(x - 0.017)^{2} + (\frac{y ^{2}}{( 0.999 ) ^{2}}) = 1

What is 16x^2+25y^2-32x-100y-284=0 ?
The solution to 16x^2+25y^2-32x-100y-284=0 is Ellipse with (h,k)=(1,2),a=5,b=4