What is ((x-1)^2)/1+((y-3)^2)/4 =1 ?

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

Popular >

((x-1)^2)/1+((y-3)^2)/4 =1

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

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

\frac{x ^{2}}{5} + \frac{y ^{2}}{3} = 1

16 x^{2} + 25 y^{2} - 64 x + 150 y - 11 = 0

\frac{( x + 3 ) ^{2}}{49} + \frac{y ^{2}}{36} = 1

25 x^{2} + 16 y^{2} - 350 x + 96 y - 231 = 0

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