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Romashka-Z-Leto [24]
2 years ago
10

Hii! I need some help, would anyone mind helping me?

Mathematics
1 answer:
Kisachek [45]2 years ago
8 0

Step-by-step explanation:

{x}^{2}  - 14x  - 25 {y}^{2}  + 100y = 76

Factor by grouping,

( {x}^{2}  - 14x)   - (25 {y}^{2}  - 100y) = 76

Complete the square, with the x variables,

( {x}^{2}  - 14x + 49)  - (25 {y}^{2}  - 100y) = 125

Factor out 25 for the y variables

( {x}^{2}  - 14x + 49) - 25( {y}^{2}  - 4y) = 125

Complete the square

( {x}^{2}  - 14x + 49) - 25( {y}^{2}  - 4y + 4) = 25

Simplify the perfect square trinomial

(x - 7) {}^{2}  - 25(y - 2) {}^{2}  = 25

Make the right side be 1 so divide everything by 25.

\frac{(x - 7) {}^{2} }{25}  -  (y - 2) {}^{2}  = 1

Here our center is (7,2).

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