158sorry the answer for 2) is (b)
1)The larger of two angles made with x-axis of a straight line drawn through(1,2) so that it intersects x+y=4 at a distance √63from (1,2) is:
(a)15° (b)60° (c)75° (d)105° (ans-(c))
2)If the straight lines ax+by+c=0 and xcosα+ysinα=c enclose an angle π4between them and meet thestraight line xsinα-ycosα=0 in the same point, then:
(a)a2+b2=c2 (b)a2+b2=2 (c)a2+b2=2c2 (d)a2+b2=4 (Ans-(c))
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3 Answers
996q1
suppose a line passing through (1,2)makes an angle A with x-axis.then its eqn is
x-1/cosA =y-2/sinA
the coordinates of pt on line at a distance
√6/3=√2/3 from (1,2)are given by
x-1/cosA =y-2/sinA=√2/3 or ,(1+√2/3*cosA ,2+
√2/3*sinA)
this pt lies on x+y =4
cosA+sinA=√3/2
sin(A+pie/4)=√3/2
A+pie/4=pie/3,2pie/3
A=pie/12,5pie/12
A=15 or 75
996q 2
the straight line xcosA+ysinA =c and xsinA-ycosA=0 are mutually perpendicular .Line xcosA+ysinA=c ,is in normal form .So, the perpendicular from the origin as this line is or length c and makes angle pie/4 with X-axis .The line xsinA-ysinA=0 passes through the origin and makes angle A with x-axis .So this is perpendicular frm origin on xcosA+ysinA =c.line ax+by+c=0(pq) makes angle pie/4 with xcosA+ysinA=c and xcosA+ysinA=c n xsinA-ysinA=0 are mutually perpendicular .So,ax+by+c =0is a bisector of the angle between them.after construction oq =opsin45
also lengthof the perpendicular from (0,0)on ax+by+c=0 is c/√a^2+b^2
on equating both we get a^2+b^2=0