Question

The equation represents an ellipse. Which points are the approximate locations of the foci of the ellipse? Round to the nearest tenth. (−8, −4.6) and (−8, 2.6) (−2.6, −8) and (4.6, 8) (1, 4.4) and (1, 11.6) (11.6, 1) and (4.4, 1)

Answer 1

The answer is C..............

Answer 2

Answer : (1, 4.4) and (1, 11.6)

Equation of ellipse is

$\frac{(y-8)^{2}}{49}$ + $\frac{(x-1)^{2}}{36}$ = 1

From the equation we know that center (h, k) is (1,8)

The equation is in the form of

$\frac{(y)^{2}}{a^2}$ + $\frac{(x)^{2}}{b^2}$ = 1

a^2= 49 so a= 7

b^2 = 36 so b= 6

To find foci , we find the distance between the center of ellipse and foci that is represented as C

We know c^2 = a^2 - b^2

Plug in the values

c^2 = 7^2 - 6^2

c^2 = 49 - 36= 13

So c= sqrt(13)= 3.61

Foci = (h, k +c) and (h, k-c)

We know h=1, k=8 and c= 3.61

(h, k+c) = (1, 8+3.61) = (1, 11.6)

(h, k-c) = (1, 8 - 3.61)= (1, 4.4)

So foci = (1, 4.4) and (1, 11.6)