What is 25x^2+4y^2+50x-16y-59=0 ?

The solution to 25x^2+4y^2+50x-16y-59=0 is Ellipse with (h,k)=(-1,2),a=2,b=5

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25x^2+4y^2+50x-16y-59=0

25 x^{2} + 4 y^{2} + 50 x - 16 y - 59 = 0

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

Solution steps

25 x^{2} + 4 y^{2} + 50 x - 16 y - 59 = 0

Rewrite

25 x^{2} + 4 y^{2} + 50 x - 16 y - 59 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

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

16 - 4 x^{(2)} - y^{(2)} \geq 0

(\frac{x}{2})^{2} + z^{2} = 1

X^{2} + Y^{2} - 4 Y \leq 0

\frac{x ^{2}}{484} + \frac{y ^{2}}{289} = 1

What is 25x^2+4y^2+50x-16y-59=0 ?
The solution to 25x^2+4y^2+50x-16y-59=0 is Ellipse with (h,k)=(-1,2),a=2,b=5