If the point P(2,2) is equidistant …
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Gaurav Seth 5 years, 4 months ago
Given points are A(-2, k), B(-2k , -3) and P(2, 2)
It is given that point P is the equidistant from the points A and B
So, PA = PB
Now,
Squaring on both sides
⇒ (- 2 - 2)2 + (k - 2)2 = (-2k - 2)2 + (-3 - 2)2
⇒ 16 + k2 + 4 - 4k = 4k2 + 4 + 8k + 25 [∵ ( a - b)2 = a2 - 2ab + b2 ]
⇒ 4k2 + 4 + 8k + 25 -16 - k2 - 4 + 4k = 0
⇒ 3k2 + 12k + 9 = 0
⇒ k2 + 4k + 3 = 0
⇒ k2 + 3k + k + 3 = 0
⇒ k(k + 3) + 1(k + 3) = 0
⇒ (k + 3) (k + 1) = 0
⇒ (k + 3) = 0 or (k + 1) = 0
∴ k = -1 or -3.
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