What is 16(x-1)^2+4(y-4)^2=64 ?

The solution to 16(x-1)^2+4(y-4)^2=64 is Ellipse with (h,k)=(1,4),a=2,b=4

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16(x-1)^2+4(y-4)^2=64

16 (x - 1)^{2} + 4 (y - 4)^{2} = 64

(h, k) = (1, 4), a = 2, b = 4

Solution steps

16 (x - 1)^{2} + 4 (y - 4)^{2} = 64

Rewrite

16 (x - 1)^{2} + 4 (y - 4)^{2} = 64

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, 4), a = 2, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, 4), b = 4, a = 2

9 x^{2} + 5 y^{2} + 18 x - 10 y - 31 = 0

\frac{( x - 3 ) ^{2}}{25} + \frac{y ^{2}}{9} = 1

\frac{( x + 5 ) ^{2}}{9} + (y - 1)^{2} = 1

4 x^{2} - 16 x + y^{2} + 2 y = - 1

4 x^{2} + 9 y^{2} = 4

What is 16(x-1)^2+4(y-4)^2=64 ?
The solution to 16(x-1)^2+4(y-4)^2=64 is Ellipse with (h,k)=(1,4),a=2,b=4