What is ((x-1)^2)/(16)+((y-4)^2)/(52)=1 ?

The solution to ((x-1)^2)/(16)+((y-4)^2)/(52)=1 is Ellipse with (h,k)=(1,4),a=4,b=2sqrt(13)

Popular >

((x-1)^2)/(16)+((y-4)^2)/(52)=1

\frac{( x - 1 ) ^{2}}{16} + \frac{( y - 4 ) ^{2}}{52} = 1

(h, k) = (1, 4), a = 4, b = 213

Solution steps

\frac{( x - 1 ) ^{2}}{16} + \frac{( y - 4 ) ^{2}}{52} = 1

Rewrite

\frac{( x - 1 ) ^{2}}{16} + \frac{( y - 4 ) ^{2}}{52} = 1

in the form of the standard ellipse equation

\frac{( x - 1 ) ^{2}}{4 ^{2}} + \frac{( y - 4 ) ^{2}}{( 2 13 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (1, 4), a = 4, b = 213

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, 4), b = 213, a = 4

x^{2} + 3 (y^{2}) = 84

\frac{2}{4} (3 x^{2} + y^{2}) - 2 (x - y) = 0

16 x^{2} + y^{2} - 64 x + 8 y + 16 = 0

\frac{1}{2} x^{2} + 6 y^{2} - 5 x + \frac{1}{4} y + 8 = 0

x^{2} + \frac{y ^{2}}{36} = 1

What is ((x-1)^2)/(16)+((y-4)^2)/(52)=1 ?
The solution to ((x-1)^2)/(16)+((y-4)^2)/(52)=1 is Ellipse with (h,k)=(1,4),a=4,b=2sqrt(13)