Question

O ponto P(3, b) pertence à circunferência de centro no ponto C(0, 3) e raio 5. Calcule valor da coordenada b.

Answer 1

Explicação passo-a-passo:

$\sf \overline{PC}=5$

$\sf \sqrt{(x_P-x_C)^2+(y_P-y_C)^2}=5$

$\sf \sqrt{(3-0)^2+(b-3)^2}=5$

$\sf \sqrt{3^2+(b-3)^2}=5$

$\sf (\sqrt{3^2+(b-3)^2})^2=5^2$

$\sf 3^2+(b-3)^2=5^2$

$\sf 9+(b-3)^2=25$

$\sf (b-3)^2=25-9$

$\sf (b-3)^2=16$

$\sf b-3=\pm\sqrt{16}$

$\sf b-3=\pm4$

• $\sf b-3=4$

$\sf b=4+3$

$\sf \red{b=7}$

• $\sf b-3=-4$

$\sf b=-4+3$

$\sf \red{b=-1}$