What is ((x+1)^2}{16}+\frac{(y+1)^2)/9 =1 ?

The solution to ((x+1)^2}{16}+\frac{(y+1)^2)/9 =1 is Ellipse with (h,k)=(-1,-1),a=4,b=3

Popular >

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

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

(h, k) = (- 1, - 1), a = 4, b = 3

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - ( - 1 ) ) ^{2}}{4 ^{2}} + \frac{( y - ( - 1 ) ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 1, - 1), a = 4, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 1, - 1), a = 4, b = 3

a^{2} + 2 b^{2} = 1

- 25 x^{2} - 4 y^{2} + 100 = 4

\frac{( x - 6 ) ^{2}}{36} + \frac{( y + 2 ) ^{2}}{100} = 1

9 x^{2} - 72 x + 4 y^{2} + 40 y + 244 = 36

(x - a)^{2} + (y - (a - 16))^{2} = 1

What is ((x+1)^2}{16}+\frac{(y+1)^2)/9 =1 ?
The solution to ((x+1)^2}{16}+\frac{(y+1)^2)/9 =1 is Ellipse with (h,k)=(-1,-1),a=4,b=3