EAMCET Engineering 2003 Solved Paper

Let co-ordinates of P be (x1,y1).
Given that,
x2+y2+2x−4y−20=0 . . . (i)
and x2+y2−4x+2y−44=0 . . . (ii)
Length of the tangent from P to Eq. (i)
=x12+y12+2x1−4y1−20 . . . (iii)
Length of the tangent from P to Eq. (ii)
=x12+y12−4x1+2y1−44 . . . (iv)
Given that ratio of lengths of tangent =‌

2

3

‌⇒‌‌‌

x12+y12+2x1−4y1−20

x12+y12−4x1+2y1−44

=‌

2

3

‌⇒‌‌3x12+3y12+6x1−12y1−60
‌=2x12+2y12−8x1+4y1−88
‌⇒‌‌x12+y12+14x1−16y1+28=0
∴ Locus of points P is
x2+y2+14x−16y+28=0
Centre of the circle is (−7,8).