Question

1. Find the area between two concentric
circles defined by
x² + y² -2x + 4y + 1 = 0
x² + y² -2x + 4y - 11 = 0


2. Find all values of parameter m
(a real number) so that the equation
2x² - mx + m = 0 has no real solutions.



@Wello1
☺☺☺

Answer 1

X² + y² - 2x + 4y + 1 = 0
x² - 2x + y² + 4y + 1 = 0
(x - 1)² - 1 + (y + 2)² - 4 + 1 = 0
(x - 1)² + (y + 2)² - 4 = 0
(x - 1)² + (y + 2)² = 4

r² = 4

x² + y² - 2x + 4y - 11 = 0
x² - 2x + y² + 4y - 11 = 0
(x - 1)² - 1 + (y + 2)² - 4 - 11 = 0
(x - 1)² + (y + 2)² - 16 = 0
(x - 1)² + (y + 2)² = 16

R² = 16

area = π(R² - r²)
= π(16 - 4)
= 12π

==========

2x² - mx + m = 0

a = 2
b = -m
c = m

b² - 4ac < 0
(-m)² - 4(2)(m) < 0
m² - 8m < 0
m(m - 8) < 0

jadi,

0 < m < 8