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

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

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

$c^2 = a^2 - b^2$

$b^2 = a^2 - c^2$

$b^2 = 5^2 - (2\sqrt{5})^2$

$b^2 = 25 - 20$

b^2 = 5

plug in all the values

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

$\frac{(x-4)^2}{25} + \frac{(y-2)^2}{5}=1$

Option B is correct