QUESTION: A point (a,b) is equidistant from the y-axis and from the point (4,0).
Find a relationship between a and b.
I thought that the equidistant points would form a sideways parabolic curve going through (2,0) as the midway point on the x-axis between (4,0) and the origin.
I thought the relationship would emerge from using the distance between points formula using; (4,0), (a,b), and (0,y) as the point on the y-axis.
sqrt((a-0)2+(b-y)2)=sqrt((4-a)2+(0-b)2)
square both sides; (a-0)2+(b-y)2=(4-a)2+(0-b)2
expand brackets: a2+b2-2by+y2=16-8a+a2+b2
cancel terms: y2-2by=16-8a
However I still have y terms involved which I don't know how to deal with.
The answer is; b2 = 8a - 16
I used this to create the graph.
Many thanks to anyone who looks through this.
Find a relationship between a and b.
I thought that the equidistant points would form a sideways parabolic curve going through (2,0) as the midway point on the x-axis between (4,0) and the origin.
I thought the relationship would emerge from using the distance between points formula using; (4,0), (a,b), and (0,y) as the point on the y-axis.
sqrt((a-0)2+(b-y)2)=sqrt((4-a)2+(0-b)2)
square both sides; (a-0)2+(b-y)2=(4-a)2+(0-b)2
expand brackets: a2+b2-2by+y2=16-8a+a2+b2
cancel terms: y2-2by=16-8a
However I still have y terms involved which I don't know how to deal with.
The answer is; b2 = 8a - 16
I used this to create the graph.
Many thanks to anyone who looks through this.
