What is 9(x+2)^2+4(y+1)^2=1 ?

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

Popular >

9(x+2)^2+4(y+1)^2=1

9 (x + 2)^{2} + 4 (y + 1)^{2} = 1

(h, k) = (- 2, - 1), a = \frac{1}{3}, b = \frac{1}{2}

Solution steps

9 (x + 2)^{2} + 4 (y + 1)^{2} = 1

Rewrite

9 (x + 2)^{2} + 4 (y + 1)^{2} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 2, - 1), a = \frac{1}{3}, b = \frac{1}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 2, - 1), b = \frac{1}{2}, a = \frac{1}{3}

\frac{( x - 1 ) ^{2}}{6} + \frac{( y - 3 ) ^{2}}{2} = 1

\frac{12 ( x ) ^{2}}{24} + \frac{3 y ^{2}}{24} = \frac{24}{24}

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

(y - 6)^{2} + 8 x^{2} = 64

x^{2} + 16 y^{2} - 128 y + 240 = 0

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