What is ((x-1)^2)/4+((y+5)^2)/(16)=1 ?

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

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((x-1)^2)/4+((y+5)^2)/(16)=1

\frac{( x - 1 ) ^{2}}{4} + \frac{( y + 5 ) ^{2}}{16} = 1

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

Solution steps

\frac{( x - 1 ) ^{2}}{4} + \frac{( y + 5 ) ^{2}}{16} = 1

Rewrite

\frac{( x - 1 ) ^{2}}{4} + \frac{( y + 5 ) ^{2}}{16} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

(\frac{x - 1}{2})^{2} + (y + 3)^{2} = \frac{49}{64}

x^{2} + y^{2} = 2 \cdot \frac{y}{x ^{2} + y ^{2}}

16 x^{2} + 25 y^{2} - 64 x - 150 y - 11 = 0

36 (x^{2} - x) + 64 (y^{2} + 4 y) + 256 = 576

\frac{( x - 2 ) ^{2}}{25} + \frac{( y - 4 ) ^{2}}{16} = 1

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