Answer:
see explanation
Step-by-step explanation:
substitute x = 2y + 5 into the equation of the circle
(2y + 5 )² + y² = 5
4y² + 20y + 25 + y² - 5 = 0
5y² + 20y + 20 = 0 ( divide all terms by 5 )
y² + 4y + 4 = 0
Use the discriminant to determine the nature of the roots
with a = 1, b = 4 and c = 4
b² - 4ac = 4² - (4 × 1 × 4 ) = 16 - 16 = 0
Since b² - 4ac = 0 there are 2 equal solutions, at
y² + 4y + 4 = 0
(y + 2 )² = 0 ⇒ y = - 2 and x = (2 × - 2 ) + 5 = 1
Hence x = 2y + 5 is a tangent to the circle with point of contact (1, - 2)
