CircleEasy
Question
Locus of the centre of circles which pass through (0, 1) & touches the line y = x is -
Options
A.(x + y)2 = 4y - 2
B.(x - y)2 = 4y - 2
C.(x + y)2 = 4x - 2
D.(x - y)2 = 4x - 2
Solution
Let the centre be (x, y), then its distance from (0, 1) is same as from y - x = 0
⇒
⇒ 2x2 + 2y2 + 2 - 4y = x2 + y2 - 2xy
⇒ x2 + y2 + 2xy = 4y - 2 ⇒ (x + y)2 = 4y - 2
⇒
⇒ 2x2 + 2y2 + 2 - 4y = x2 + y2 - 2xy
⇒ x2 + y2 + 2xy = 4y - 2 ⇒ (x + y)2 = 4y - 2
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