find the distance between A(at^2,2at1) B(at2^2,2at2).
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Answers
Step-by-step explanation:
Given:-
The points are A(at1^2,2at1) B(at2^2,2at2).
To find:-
find the distance between A(at1^2,2at1) B(at2^2,2at2).
Solution:-
Given points are A(at1^2,2at1) ,B(at2^2,2at2).
Let (x1, y1)=A(at^2,2at1) =>x1=at1^2 and y1=2at1
and (x2, y2)=B(at2^2,2at2).=>x2=at2^2 and y2=2at2
We know that
The distance between the two points (x1, y1)and (x2, y2) is√[(x2-x1)^2+(y2-y1)^2] units
The distance between A and B = AB
=>√[(at2^2-at1^2)^2+(2at2-2at1)^2]
=>AB=√[{a(t2^2-t1^2)}^2+{2a(t2-t1)}^2]
=>AB=√[a^2(t2^2-t1^2)^2+4a^2(t2-t1)^2]
=>AB=√[a^2{(t2^2-t1^2)}^2+4(t2-t1)}^2]
=>AB=a√[{(t2^2-t1^2)}^2+4(t2-t1)}^2]
=>AB=a√[{(t2+t1)^2(t2-t1)^2}+4(t2-t1)^2]
=>AB=a√[(t2-t1)^2{(t2+t1)^2+4}]
=>AB=a(t2-t1)√[(t2+t1)^2+4] units
Answer:-
The distance between them is
a(t2-t1)√[(t2+t1)^2+4] units
Used formulae:-
The distance between the two points (x1, y1)and (x2, y2) is√[(x2-x1)^2+(y2-y1)^2] units