Question and Answers Forum

All Questions      Topic List

Coordinate Geometry Questions

Previous in All Question      Next in All Question      

Previous in Coordinate Geometry      Next in Coordinate Geometry      

Question Number 196917 by peter frank last updated on 03/Sep/23

Answered by MM42 last updated on 03/Sep/23

((∣PA∣)/(∣PB∣)) = 3 ✓

∣PA∣∣PB∣=3✓

Commented by peter frank last updated on 03/Sep/23

how

how

Commented by MM42 last updated on 03/Sep/23

PA=(√((a+b−4b+2a)^2 +(9c−a−3c−5a)^2 )) =3(√((a−b)^2 +4(a−c)^2 )) PB=(√((4b−2a−5b+3a)^2 +(9c−a−11c+3a)^2 )) =(√((a−b)^2 +4(a−c)^2 )) ⇒((∣PA∣)/(∣PB∣)) =3

PA=(a+b−4b+2a)2+(9c−a−3c−5a)2=3(a−b)2+4(a−c)2PB=(4b−2a−5b+3a)2+(9c−a−11c+3a)2=(a−b)2+4(a−c)2⇒∣PA∣∣PB∣=3

Commented by peter frank last updated on 05/Sep/23

thank you.

thankyou.

Answered by som(math1967) last updated on 03/Sep/23

let PA:PB=m:n ((m(5b−3a)+n(a+b))/(m+n))=4b−2a ⇒m(5b−3a)−m(4b−2a) =n(4b−2a)−n(a+b) ⇒m(b−a)=n×3(b−a) ⇒m:n=3:1 [when a≠b]

letPA:PB=m:nm(5b−3a)+n(a+b)m+n=4b−2a⇒m(5b−3a)−m(4b−2a)=n(4b−2a)−n(a+b)⇒m(b−a)=n×3(b−a)⇒m:n=3:1[whena≠b]

Commented by JDamian last updated on 03/Sep/23

3:2 where does that 2 come from?

3:2wheredoesthat2comefrom?

Commented by som(math1967) last updated on 03/Sep/23

sorry typo

sorrytypo

Answered by Nimnim111118 last updated on 05/Sep/23

Clearly, APB is a line. So, required ratio=(((4b−2a)−(a+b))/((5b−3a)−(4b−2a)))=((3b−3a)/(b−a))=(3/1) Idea: If A(x_1 ,y_1 ),P(x,y) and B(x_2 ,y_2 ) form a line then ((AP)/(PB))=((x−x_1 )/(x_2 −x))=((y−y_1 )/(y_2 −y))

Clearly,APBisaline.So,requiredratio=(4b−2a)−(a+b)(5b−3a)−(4b−2a)=3b−3ab−a=31Idea:IfA(x1,y1),P(x,y)andB(x2,y2)formalinethenAPPB=x−x1x2−x=y−y1y2−y

Commented by peter frank last updated on 05/Sep/23

thank you

thankyou

Terms of Service

Privacy Policy

Contact: info@tinkutara.com