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NISA [10]
3 years ago
10

Workout the 11th triangular number​

Mathematics
1 answer:
Arturiano [62]3 years ago
4 0
The 11th triangular number = 66
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Focus of the parabola is (-5,5) and directrix is y = -1.

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\sqrt{(x+5)^2+(y-5)^2} = \sqrt{(y+1)^2} \\\\(x+5)^2+(y-5)^2=(y+1)^2 \\\\(x+5)^2 + y^2 - 10y +25 = y^2 +2y +1 \\\\(x+5)^2 =  -y^2 +10y -25 + y^2 +2y +1 \\\\(x+5)^2 = 12y -24 \\\\12y =  (x+5)^2  +24 \\\\ y = \frac{1}{12} (x+5)^2  +2

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15 because if you substitute -1 in for x then you have a double negative, that becomes positive and 2+1=3 and 3•5=15
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