What is 4x^2+25y^2+24x+250y=-561 ?

The solution to 4x^2+25y^2+24x+250y=-561 is Ellipse with (h,k)=(-3,-5),a=5,b=2

Popular >

4x^2+25y^2+24x+250y=-561

4 x^{2} + 25 y^{2} + 24 x + 250 y = - 561

(h, k) = (- 3, - 5), a = 5, b = 2

Solution steps

4 x^{2} + 25 y^{2} + 24 x + 250 y = - 561

Rewrite

4 x^{2} + 25 y^{2} + 24 x + 250 y = - 561

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 3, - 5), a = 5, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 3, - 5), a = 5, b = 2

x^{2} - 8 x + 16 y^{2} - 2 y + 4 = 625

9 x^{2} + 25 y^{2} - 36 x - 50 y - 164 = 0

x^{2} - 2 x^{2} - 2 y^{2} - 12 = 0

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

\frac{( y - 2 ) ^{2}}{9} + \frac{( x - 3 ) ^{2}}{16} = 1

What is 4x^2+25y^2+24x+250y=-561 ?
The solution to 4x^2+25y^2+24x+250y=-561 is Ellipse with (h,k)=(-3,-5),a=5,b=2