A straight line through A ( 6 , 8 ) meets the curve 2 x 2 + y 2 = 2 at B and C . P is a point on BC such that AB , AP , AC are in H.P, then the minimum distance of the origin from the locus of '

Question

A straight line through A ( 6 , 8 ) meets the curve 2 x 2 + y 2 = 2 at B and C . P is a point on BC such that AB , AP , AC are in H.P, then the minimum distance of the origin from the locus of ' P ' is

TestHub · Accepted Answer

( 6 + r cos θ , 8 + r sin θ ) lies on 2 x 2 + y 2 = 2 ⇒ ( 2 cos 2 θ + sin 2 θ ) r 2 + 2 ( 12 cos θ + 8 sin θ ) r + 134 = 0 AB , AP , AC are in H.P ⇒ r 2 ​ = AB ⋅ AC AB + AC ​ ⇒ r 1 ​ = − 67 ( 6 c o s θ + 4 s i n θ ) ​ ⇒ 6 x + 4 y − 1 = 0 Minimum distance from ' O ' = 52 ​ 1 ​

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