Parabola y 2 = 4 √ 6x = 2px

Solution: p=2√6

Right focus f (√ 6,0)

Then the ellipse satisfies: c? =a？ -B? =6

When x=√6, the chord length is 2 and the half chord length is 1.

Point (√6 1) and point (√6 1) are on the ellipse:

6/a？ + 1/b？ = 1

So:

6/(b？ +6)+ 1/b？ = 1

Solution: b? =3 (negative value does not conform to discard)

So: a? =9

The ellipse is: x? /9+y？ /3= 1