Question

the distance between the points (t1^2 , 2t1) and (t2 ^2 , 2t2) where t1 and t2 are the roots of the equation x^2-2root3x+2=0

Answer 1

Answer:

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Answer 2

Answer:

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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