Question

The equation of the three circles are given x² + y² = 1 ,x² + y² –8x+15 =0, x² + y² +10y+24 = 0. Determine the coordinates of the point P such that the tangents drawn from it to the circles are equal in length

Answer 1

We know that the point from which lengths of tangents are equal in length is radical centre of the given three circles Radical axis of first two circles is

S₁ –S₂ = 0

8x–16 = 0 or x–2 = 0___________________(1)

and radical axis of second and third is

–8x–10y–9 = 0_________________________(2)

Solving (1) and (2) equations we get

x=2, –16–10y–9 = 0

10y = –25

y = \(\frac{-25}{10}=\frac{-5}{2} \)

∴ Radical centre P is (2, –5/2)