Question

Two points A and B have coordinates (1, 0) and

(–1, 0) respectively and Q is a point which satisfies the

relation $AQ - BQ = \pm 1.$ The locus of Q is.

• A. $12x^{2} + 4y^{2} = 3$
• B. $12x^{2} - 4y^{2} = 3$
• C. $12x^{2} - 4y^{2} + 3 = 0$
• D. $12x^{2} + 4y^{2} + 3 = 0$

Answer 1

Answer: (B)

$12x^{2} - 4y^{2} = 3$

Answer 2

According to the given condition

$\sqrt { ( x - 1 ) ^ { 2 } + y ^ { 2 } } - \sqrt { ( x + 1 ) ^ { 2 } + y ^ { 2 } } = \pm 1$

On squaring both sides, we get

$2 x ^ { 2 } + 2 y ^ { 2 } + 1 = 2 \sqrt { ( x - 1 ) ^ { 2 } + y ^ { 2 } } \cdot \sqrt { ( x + 1 ) ^ { 2 } + y ^ { 2 } }$

Again on squaring, we get

$12 x ^ { 2 } - 4 y ^ { 2 } = 3$.