a question from st. lines

from 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...

(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

consider 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.