What is the length between PO, PQ, OQ have to be when the points form a equilateral triangle?

There are 2 lines on a cartesian axis. One line is defined by Y=2X+1 and point O and Q are an element of it. The other line is described as y=2X+2 and point P is an element of it.

1 Answer
Deepak Pandey
Aug 1, 2017

#2/sqrt15#

Explanation:

The lines would be as shown
graph{4x^2+y^2-4xy+6x-3y+2=0 [-11.84, 8.16, -8.96, 1.04]}
Now as we have to choose two points on one line and one point on another one
Also we see that both the lines are parallel
#:. # Distance between these two lines will be equal to tbe length of the altitude of the triangle
#:.# Distance, #d=(2-1)/sqrt (2^2+1)=1/sqrt5#
Now length of side of triangle #=2d/sqrt3#
#=2/sqrt15#

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