What is (y-6)^2=23-(23(x-3)^2)/(39) ?

The solution to (y-6)^2=23-(23(x-3)^2)/(39) is Ellipse with (h,k)=(3,6),a=sqrt(39),b=sqrt(23)

Popular >

(y-6)^2=23-(23(x-3)^2)/(39)

(y - 6)^{2} = 23 - \frac{23 ( x - 3 ) ^{2}}{39}

(h, k) = (3, 6), a = 39, b = 23

Solution steps

(y - 6)^{2} = 23 - \frac{23 ( x - 3 ) ^{2}}{39}

Rewrite

(y - 6)^{2} - 23 + \frac{23 ( x - 3 ) ^{2}}{39} = 0

in the form of the standard ellipse equation

\frac{( x - 3 ) ^{2}}{( 39 ) ^{2}} + \frac{( y - 6 ) ^{2}}{( 23 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (3, 6), a = 39, b = 23

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (3, 6), a = 39, b = 23

\frac{x ^{2}}{1.58 7 ^{2}} + \frac{y ^{2}}{0.9 9 ^{2}} = 1

9 \cdot (x - 1)^{2} + 4 \cdot y^{2} = 36

4 x^{2} + 9 y^{2} - 144 = 0

3 x^{2} + 2 y^{2} - 8 = 0

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

What is (y-6)^2=23-(23(x-3)^2)/(39) ?
The solution to (y-6)^2=23-(23(x-3)^2)/(39) is Ellipse with (h,k)=(3,6),a=sqrt(39),b=sqrt(23)