Question

A point P moves in such a way that the ratio of its distance form two coplanar points is always a fixed number ( ≠ 1) then its locus is

(a) Straight line

(b) circle

(c) Parabola

(d) a pair of Straight lines

Answer 1

Let two coplanar points be (0, 0) and (a, 0) according to the question we get

\(\frac{AP}{BP}=\lambda (constant)\)

\(\frac{\sqrt{X^2+Y^2}}{\sqrt{(X-a)^2+Y^2}}=\lambda\)

x² +y² = λ ²(x² +y² –2ax+a²)

x² +y² +\(\frac{\lambda^2}{1-\lambda^2}(2ax-a^2)=0\)

represents equation of a circle