Answer:
x - ( 16 , 0 ) , ( -16 , 0 )
y - ( 0 , 4√7 ) , ( 0 , -4√7)
Explanation:
Solution:
- The sum of the distances from a point on the ellipse to its foci is constant. You have both foci and a point, so you can find the sum of the distances.
-Then you can find the vertices since they are points on the ellipse on the x-axis whose sum of distances to the foci are that value.
- The 7 in y coordinate of (12,7) is the length of semi-latus rectum. Also c is 12:
c^2 = a^2 + b^2
Where, a: x-intercept
b: y-intercept
- The length of semi-latus rectum is given by:
b^2 = 7*a
- Substitute latus rectum expression in the first one we get:
c^2 = a^2 + 7a
a^2 + 7a - 144 = 0
( a - 16 ) * ( a - 9 ) = 0
a = +/- ( 16 )
- The y-intercept we will use latus rectum expression again:
b = +/- √(7*16)
b = +/- 4√7
- The intercepts are:
x - ( 16 , 0 ) , ( -16 , 0 )
y - ( 0 , 4√7 ) , ( 0 , -4√7)