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My Notes

Find an equation for the conic section with the given properties.The hyperbola with center

C(2, 4), vertices V₁(2, 1) and V₂(2, 9), and foci F₁(2, 3) and F₂(2, 11)

Solution

Centre C (-2,4)   V1 (-2,-1)   V2=(-2,-9)   focii F1(-2,-3) F2 (-2,11)

This is of the form

(y-k)²/a²-(x-h)²/b²=1

where vertices = (h,k+-a)

And h=-2 and k=4

Therefore k+a= 9

           a=5

And focii= (h,k+-c)

k+c=11

c=7

c²=a²+b²

49-25=b^2

b^2=24

Therefore required equation is

(y-4)²/25 - (x+2)²/24=1