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2 years ago

25x^2+9y^2+72y-81=0. Find the standard form of the equation by completing the square. Then identify and graph each conic.

1 answer:

8 0

25x² + 9y² + 72y - 81 = 0
 25x² + 9y² + 72y - 81 + 81 = 0 + 81
 25x² + 9y² + 72y = 81
 25x² + 9(y² + 8y + 16) = 81 + 9(16)
 25x² + 9(y² + 4y + 4y + 16) = 81 + 144
 25x² + 9(y(y) + 4(y) + 4(y) + 4(4)) = 225
 25x² + 9(y(y + 4) + 4(y + 4)) = 225
 25x² + 9(y + 4)(y + 4) = 225
 25x² + 9(y + 4)² = 225
 225 225 225
 x² + 9(y + 4)² = 1
 25 25

The conic section is an ellipse.

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Proved

Step-by-step explanation:

From the given parameters, we have:

$n = 9$ i.e. the length of each security numbers

$r = 2$ i.e. 2 security numbers

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In 513 security numbers, 2 must have matching zeros

To do this, we make use of Pigeonhole principle.

First, we calculate the number of all security numbers not having matching zeros.

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