Find the equation of the line passing through the point (2,3) and making an intercept of length 3 units between the lines y+2x=2 and y+2x=5.
Plz show with steps...
21from parametric equations u will get 2 points at a distance say R and R+2, the pts will satisfy the given equations of lines....from that u will get the equations..der will b 2 lines...
23(y+2x-2)(y+2x-5) = 0 (1)....eqn of pair of given lines
parametric form of pt of intersections of line passing thru 2,3 and cutting the 2 lines,
x= 2+rcosθ , y = 3+rsinθ
put dis in (1)
and get a quadratic in r ,
now if roots of this quad are r1,r2
then we hav |r1 - r2 | = 3
i.e √(r1+r2)2 - 4r1r2 = 3
where r1 + r2 = sum of roots
r1r2 = product of roots
so u wil get some trigonometric equation,
frm that find tanθ , and then use y - 3 = tanθ (x-2)
dis is the eqn of reqd line
1consider a fixed pt P(5,2) and Q and R be two distinct variable pts on x-y=0and y=0 respectively. Find the minimum value of PQ+QR+PR.