Question

If A(2,0) and B(0, 3) are two points, find
the equation of the locus of point P such
that AP = 2BP.
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Answer 1

✪ᴀɴsᴡᴇʀ✪

• $\boxed{3x² + 3y² + 4x-24y+32=0}$

★ᴇxᴘʟᴀɪɴᴀᴛɪᴏɴ★

Let co-ordinate of P be (x,y).

Co-ordinate of A and B are (2,0) and (0,3)

Now,

$AP = 2BP$

$AP² = 4BP²$

$(x-2)² + (y-0)² = 4[(x-0)² + (y-3)²]$

$x²-4x+4 + y² = 4[x² + y²-6y+9]$

$x²-4x+4 + y² = 4x² + 4y²-24y+36$

$3x² + 3y² + 4x-24y+32=0$

The locus is a circle.