if lines px2-qxy-y2=0, make angles alpha n beta with X- axis then value of: tan ( alpha+beta) = ?
a) -p/1+q
b) -q/1+p
c) q/1+p
d) p/1+q

Question

if lines px2-qxy-y2=0, make angles alpha n beta with X- axis then
value of: tan ( alpha+beta) = ?
a) -p/1+q
b) -q/1+p
c) q/1+p
d) p/1+q

Tanveer Sofi · Accepted Answer

The equation of the pair of staight lines ispx2-qxy-y2=0For, general form of equation of pair of straight lines  ax2+2hxy+by2=0,if tan α1 and tan α2 are the slopes of the two lines represented by above equation,then tan α1+ tan α2=-coefficient of xycoefficient of y2=-2hb tan α1× tan α2=coefficient of x2coefficient of y2=abNow, for the given pair of straight lines, px2-qxy-y2=0, we havetan α+tan β=--q-1=-qtan α×tan β=p-1=-pTherefore,tanα+β=tan α+tan β1-tan α×tan β=-q1--p=-q1+pHence, option  b is correct

if lines px2-qxy-y2=0, make angles alpha n beta with X- axis then value of: tan ( alpha+beta) = ? a) -p/1+q b) -q/1+p c) q/1+p d) p/1+q

if lines px2-qxy-y2=0, make angles alpha n beta with X- axis then value of: tan ( alpha+beta) = ?
a) -p/1+q
b) -q/1+p
c) q/1+p
d) p/1+q