Locus of mid-point of the chords of contact of x2 + y2 = 2 from the points on the line 3x + 4y = 10 is a circle with centre P. If O be the origin then OP is equal to
Chord with mid-point (h, k) is
hx + ky = h2 + k2 …(1)
chord of contact of (x1, y1) is
xx1 + yy1 = 2 …(2)
Comparing, we get
(x1, y1) lies on 3x + 4y = 10 ⇒ 6h + 8k = 10(h2 + k2)
∴ locus of (h, k) is
∴ OP = 1/2.
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