UPSEE Solved Model Paper 5

Let p(x1,y1) be any point on the circle x2+y2+2gx+2fy = c = 0
Then , the length of the tangents drawn from p(x1,y1) to the circle
x2+y2 + 2gx + 2fy + csin2α+(g2+f2)cos2α = 0 is PQ = PR

=
= √−x+csin2α+(g2+f2)cos2α
= √g2+f2−c cos α
The radius of the circle x2+y2 + 2gx + 2fy = csin2α + (g2+f2)cos2α = 0
is CQ = CR
= √g2+f2−csin2α−(g2+f2)cos2α
= √g2+f2−csinα
In ΔPQC ,
tan θ =

CO

PQ

⇒ tan θ =

√(g2+f2−c)sinα

√(g2+f2−c)cosα

= tan α ⇒ θ = α