Question

Determine o valor de a de modo que o ponto P ( 1, a ) pertença à circunferência

X2 + y2 - 2x – 5y + 7 = 0.

Answer 1

P(1,a)

x² + y² - 2x - 5y + 7 = 0

(1)² + a² - 2 . (1) - 5 . (a) + 7 = 0

1 + a² - 2 - 5a + 7 = 0

a² - 5a + 6 = 0

Δ = b² - 4ac

Δ = 25 - 4 . (1) . (6)

Δ = 25 - 24

Δ = 1

$a = \frac{-b \frac{+}{-} \sqrt{b^2-4ac} }{2a}$

$a = \frac{-(-5) \frac{+}{-} \sqrt{1} }{2}$

$a = \frac{5 \frac{+}{-}1 }{2}$

$a' = \frac{5 + 1 }{2}$

$a' = \frac{6 }{2}$

a' = 3

$a" = \frac{5 - 1 }{2}$

$a" = \frac{4 }{2}$

a" = 2

S = {2,3}