Question

If M (x, y) is equidistant from A (a + b, b – a) and B (a – b, a + b), then

(a) bx + ay = 0

(b) bx – ay = 0

(c) ax + by = 0

(d) ax – by = 0

Answer 1

Correct option is (b) bx – ay = 0

Let, M(x, y) is equidistant from the points A(a + b, b − a) and B(a − b, a + b).

We know, distance between (x₁​, y₁​) and (x₂​, y₂​) = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

Distance between point M and point A,

Distance between point M and point B,

Point M(x, y) is equidistant from the points A(a + b, b − a) and B(a − b, a + b).

∴ MA = MB

⇒ MA² = MB²

⇒ −2ax − 2bx − 2by + 2ay = −2ax + 2bx − 2by − 2ay

From (1) and (2),

⇒ −2bx + 2ay = 2bx − 2ay

⇒ 4bx − 4ay = 0

⇒ bx − ay = 0