What is ((x+5)^2)/4+((y-1)^2)/(25)=1 ?

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

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((x+5)^2)/4+((y-1)^2)/(25)=1

\frac{( x + 5 ) ^{2}}{4} + \frac{( y - 1 ) ^{2}}{25} = 1

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

Solution steps

\frac{( x + 5 ) ^{2}}{4} + \frac{( y - 1 ) ^{2}}{25} = 1

Rewrite

\frac{( x + 5 ) ^{2}}{4} + \frac{( y - 1 ) ^{2}}{25} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

25 x^{2} + 36 y^{2} - 350 x + 350 = 0

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

15 x^{2} + 15 y^{2} + 16 y \geq 0

\frac{( y - 3 ) ^{2}}{64} + \frac{( x + 5 ) ^{2}}{81} = 1

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

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