[tex]\large{\mathcal{SOLUTION:}}[/tex]
In the equation (x-h)² = 4a(y-k)
- The length of the latus rectum is 4a
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We convert the equation the standard form of parabola
- x²+8x = 12y-36
- (x²+8x+16) = 12y-36 - 16
- (x+4)² = 12y-20
- (x+4)² = 12(y-20/12)
- (x-4)² = 12(y-5/3)
In the standard form , we can see that 4a = 12 Therefore , the length of the latus rectum is 12
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[tex]\large{\mathcal{ANSWER:}}[/tex]
