What is 16X^2+25Y^2-64X-50Y-311=0 ?

The solution to 16X^2+25Y^2-64X-50Y-311=0 is Ellipse with (h,k)=(2,1),a=5,b=4

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16X^2+25Y^2-64X-50Y-311=0

16 X^{2} + 25 Y^{2} - 64 X - 50 Y - 311 = 0

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

Solution steps

16 X^{2} + 25 Y^{2} - 64 X - 50 Y - 311 = 0

Rewrite

16 X^{2} + 25 Y^{2} - 64 X - 50 Y - 311 = 0

in the form of the standard ellipse equation

\frac{( X - 2 ) ^{2}}{5 ^{2}} + \frac{( Y - 1 ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

7 x^{2} + 9 y^{2} = 1

\frac{x ^{2}}{2.3 2 ^{2}} + \frac{y ^{2}}{2.8 2 ^{2}} = 1

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

\frac{( x - 4 ) ^{2}}{9} + \frac{( y - 5 ) ^{2}}{4} = 1

- 8 y^{2} + 72 = 9 x^{2}

What is 16X^2+25Y^2-64X-50Y-311=0 ?
The solution to 16X^2+25Y^2-64X-50Y-311=0 is Ellipse with (h,k)=(2,1),a=5,b=4