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

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

Popular >

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

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

(h, k) = (2, 1), a = 2, b = 3

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, 1), a = 2, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, 1), b = 3, a = 2

x^{2} - 2 x + \frac{y ^{2}}{4} - y = 14

\frac{( x + 1 ) ^{2}}{28} + \frac{( y + 5 ) ^{2}}{23} = 1

2 x^{2} + y^{2} + 12 x - 2 y + 17 = 0

y^{2} + 2 y + 6 x^{2} - 12 x = 1

x^{2} + 2 y^{2} - 2 x - 4 y - 5 = 0

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