Geometry

2D Coordinate Geometry

Distance between point and line

         

If point (p,0)(p,0) is equidistant from the two lines 9xy+1=0,x9y5=09x-y+1=0, x-9y-5=0 and p>0p>0, what is p?p?

Consider point A=(a,2)A=(a,2) with a>0a > 0 such that over all points PP on the line x4+y3=1,\frac{x}{4}+\frac{y}{3}=1, the minimum value of AP\overline{AP} is 2.2. What is the value of 3a?3a?

Given a point PP on the positive xx-axis such that the distance between PP and the line 4x+3y+6=04x+3y+6=0 is 10,10, what are the coordinates of P?P ?

If real numbers  a \ a\ and  b \ b\ satisfy a2+b2=49 a^2 + b^2 = 49 , what is the distance between the lines ax+by=1      and      ax+by=225? ax + by = 1\;\;\; \textrm{and} \;\;\; ax + by = 225 ?

If point (p,0)(p,0) is equidistant from the two lines 12xy+1=0,x12y4=012x-y+1=0, x-12y-4=0 and p>0p>0, what is p?p?

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