The focal distances of the point 4 5 , 3 5 on the ellipse x 2 4 + y 2 9 = 1 are

Step-by-step solution

Given, Equation of ellipse x 2 4 + y 2 9 = 1 , So we can see b > a so it is vertical ellipse, Hence eccentricity is given by a 2 = b 2 1 - e 2 , ⇒ 4 = 9 1 - e 2 ⇒ e = 5 3 Now focus is given by 0 , ± b e ≡ 0 , ± 5 Now assuming S ≡ 0 , 5   &   S ' ≡ 0 , - 5 and point P 4 5 , 3 5 , Now focal distance will be P S   &   P S ' , Now using distance formula we get, P S = 4 5 - 0 2 + 3 5 - 5 = 4 = 2 And similarly P S ' = 4