What is 25x^2+16y^2+200x-160y+400=0 ?

The solution to 25x^2+16y^2+200x-160y+400=0 is Ellipse with (h,k)=(-4,5),a=4,b=5

Popular >

25x^2+16y^2+200x-160y+400=0

25 x^{2} + 16 y^{2} + 200 x - 160 y + 400 = 0

(h, k) = (- 4, 5), a = 4, b = 5

Solution steps

25 x^{2} + 16 y^{2} + 200 x - 160 y + 400 = 0

Rewrite

25 x^{2} + 16 y^{2} + 200 x - 160 y + 400 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 4, 5), a = 4, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

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

4 x^{2} + 9 y^{2} - 48 x + 72 y = - 144

4 - x^{2} - 4 y^{2} \geq 0

\frac{( x + 5 ) ^{2}}{9} + \frac{( y - 4 ) ^{2}}{36} = 1

\frac{x ^{2}}{9} + \frac{y ^{2}}{45} = 1

What is 25x^2+16y^2+200x-160y+400=0 ?
The solution to 25x^2+16y^2+200x-160y+400=0 is Ellipse with (h,k)=(-4,5),a=4,b=5