Question

If a point P is moving such that the
length of tangents drawn from P to
x² + y^2 - 2x + 4y - 20 =0,
x^2 + y^2 - 2x - 8y +1=0 are in the ratio 2:
1 then locus of P is​

Answer 1

Answer:

S1 = x² + y² - 2x + 4y - 20 = 0

S2 = x² + y² - 2x - 8y + 1 = 0

PA/PB = 2/1

Let P(x1, y1)

PA = 2PB

√(x1² + y1² - 2x1 + 4y1 - 20) = 2√(x1² + y1² - 2x1 - 8y1 + 1)

3x1² + 3y1² - 6x1 - 36y1 + 24 = 0

x1² + y1² - 2x1 - 12y1 + 8 = 0

Therefore locus of P is -

x² + y² - 2x - 12y + 8 = 0