Question

6. A variable circle is drawn to touch the line \( 3 x-4 y=10 \) and also the circle \( x^{2}+y^{2}=1 \) externally then the locus of its centre is - (A) straight line (B) circle (C) pair of real, distinct straight lines (D) parabola PR0006

Answer 1

Consider a line L₂ , 2 units to left of L₁  and parallel to L₁.

Therefore, distance of centre of circle C from L₂

 =2+r

And, distance of C from origin = 2+r

Therefore, locus of C is a parabola.