(at^2,2at) is a point on the line 2x-5y+12a=0,from this find the co-ordinates of two points on the line?

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Answer 1 · 2017-08-03T09:05:28

The two points are #(4a,4a)# and #(9a,6a)#.

As #(at^2,2at)# is a point on the line #2x-5y+12a=0#,

we have #2at^2-10at+12a=0#

or assuming #a!=0#, we have

#t^2-5t+6=0#

or#(t-3)(t-2)=0#

i.e. #t=3# or #2#

Hence two points are #(a3^2,2a*3)# i.e. #(9a,6a)#

and #(a2^2,2a*2)# i.e. #(4a,4a)#

if #a=1#, these appear as below

graph{(y^2-4x)(2x-5y+12)((x-9)^2+(y-6)^2-0.02)((x-4)^2+(y-4)^2-0.02)=0 [1.04, 11.04, 2.12, 7.12]}