What is ((y+1)^2}{16}+\frac{x^2)/4-1=0 ?

The solution to ((y+1)^2}{16}+\frac{x^2)/4-1=0 is Ellipse with (h,k)=(0,-1),a=2,b=4

Popular >

((y+1)^2}{16}+\frac{x^2)/4-1=0

\frac{( y + 1 ) ^{2}}{16} + \frac{x ^{2}}{4} - 1 = 0

(h, k) = (0, - 1), a = 2, b = 4

Solution steps

\frac{( y + 1 ) ^{2}}{16} + \frac{x ^{2}}{4} - 1 = 0

Rewrite

\frac{( y + 1 ) ^{2}}{16} + \frac{x ^{2}}{4} - 1 = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{2 ^{2}} + \frac{( y - ( - 1 ) ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, - 1), a = 2, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, - 1), b = 4, a = 2

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

\frac{x ^{2}}{8 ^{2}} + \frac{y ^{2}}{5 ^{2}} = 1

x^{2} - 4 x + 4 y^{2} + 4 y + 1 = 0

25 x^{2} + 49 y^{2} = 49

x^{2} + x + 2 y^{2} + y - 1 = 0

What is ((y+1)^2}{16}+\frac{x^2)/4-1=0 ?
The solution to ((y+1)^2}{16}+\frac{x^2)/4-1=0 is Ellipse with (h,k)=(0,-1),a=2,b=4