the distance between the points (at1^2 , 2at1) and (at2 ^2 , 2at2) where t1 and t2 are the roots of the equation x^2-2root3x+2=0 and a>0 is
Answers
Answer:
Step-by-step explanation in the attachment
8a is the distance between the points (at1² , 2at1) and (at2² , 2at2)
Step-by-step explanation:
t1 and t2 are the roots of the equation x²-2√3x+2=0
x = (2√3 ± √(12 - 8))/2
=> x = √3 ± 1
t1 = √3 + 1 t2 = √3 - 1
t1 - t2 = ±2
=> (t1 - t2)² = 4
t1 + t2 = 2√3
(t1 + t2)² = 12
the distance between the points (at1² , 2at1) and (at2² , 2at2)
= √(at2² - at1²)² + (2at2 - 2at1)²
= √a²((t2 + t1)(t2 - t1)² + 4*a²(t2 - t1)²
= √a²((t2 + t1)²(t2 - t1)² + 4*a²(t2 - t1)²
= √a²12*4 + 4*a²*4
= √64a²
= 8a
8a is the distance between the points (at1² , 2at1) and (at2² , 2at2)
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