What is 5(x-3)^2=20-4(y-6)^2 ?

The solution to 5(x-3)^2=20-4(y-6)^2 is Ellipse with (h,k)=(3,6),a=2,b=sqrt(5)

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5(x-3)^2=20-4(y-6)^2

5 (x - 3)^{2} = 20 - 4 (y - 6)^{2}

(h, k) = (3, 6), a = 2, b = 5

Solution steps

5 (x - 3)^{2} = 20 - 4 (y - 6)^{2}

Rewrite

5 (x - 3)^{2} - 20 + 4 (y - 6)^{2} = 0

in the form of the standard ellipse equation

\frac{( x - 3 ) ^{2}}{2 ^{2}} + \frac{( y - 6 ) ^{2}}{( 5 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (3, 6), a = 2, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (3, 6), b = 5, a = 2

16 x^{2} + 36 y^{2} = 576

x^{2} + \frac{y ^{2}}{4} < 1

16 x^{2} + 25 y^{2} = 1

4 x^{2} + 2 y^{2} - 8 x + 12 y + 6 = 0

\frac{( x + 3 ) ^{2}}{25} + \frac{( y - 8 ) ^{2}}{16} = 1

What is 5(x-3)^2=20-4(y-6)^2 ?
The solution to 5(x-3)^2=20-4(y-6)^2 is Ellipse with (h,k)=(3,6),a=2,b=sqrt(5)