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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

10 x^{2} + 40 x + 7 y^{2} + 70 y + 145 = 0

4 x^{2} + 4 y^{2} = 100 - 20 x + x^{2}

6 = x^{2} + 9 y^{2}

1 = \frac{( x - 3 ) ^{2}}{16} + \frac{y ^{2}}{4}

(3 x - 3)^{2} + (- 2 y - 4)^{2} = 43 + 9 + 16

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