Question

The point on the x-axis which is equidistant from points (−1, 0) and (5, 0) is

विकल्प

•  (0, 2)   

•  (2, 0)      

• (3, 0)     

• (0, 3)

Answer 1

Let A(−1, 0) and B(5, 0) be the given points. Suppose the required point on the x-axis be P(x, 0).
It is given that P(x, 0) is equidistant from A(−1, 0) and B(5, 0).
∴ PA = PB
⇒ PA² = PB² $$\Rightarrow {[x-(-1)]}^2+{(0-0)}^2={(x-5)}^2+{(0-0)}^2$$            (Using distance formula)

$$\Rightarrow {(x+1)}^2={(x-5)}^2$$
$$\Rightarrow x^2+2x+1=x^2-10x+25$$
$$\Rightarrow 12x=24$$
$$\Rightarrow x=2$$

Thus, the required point is (2, 0).