Question

Write the equation of the ellipse with center (4,2), vertex (9,2), and focus (4+2sqrt5,2)

Answer 1

Answer : option B

Given: center (4,2), vertex (9,2), and focus (4+2sqrt5,2)

The distance between vertex and center is 9-4 = 5

Center is (h,k) so h= 4 and k =2

focus is (h+c,k)

From the given focus (4+2sqrt5,2), c= 2sqrt(5)

Standard form of equation is

`((x-h)^2)/(a^2) + ((y-k)^2)/(b^2)=1`

h= 4, k=2, a=5, c=2sqrt(5), we need to find out b

`c^2 = a^2 - b^2`

`b^2 = a^2 - c^2`

`b^2 = 5^2 - (2√(5))^2`

`b^2 = 25 - 20`

b^2 = 5

plug in all the values

`((x-h)^2)/(a^2) + ((y-k)^2)/(b^2)=1`

`((x-4)^2)/(25) + ((y-2)^2)/(5)=1`

Option B is correct