Let a line through the point P(5,10) cut the line l whose equation is x+2y=5, at Q and the circle C whose equation is x^2+y^2=25, at A and B. Then

JEE Advanced Mathematics question

Let a line through the point cut the line whose equation is , at Q and the circle whose equation is , at A and B. Then

(A)P is the pole of the line with respect to the circle Correct
(B) is the pllar [sic — *polar*] of the point P with respect to the circle Correct
(C) are in AP
(D) is the HM of and Correct

Answer: (A),(B),(D)

The polar of w.r.t. is , i.e. , which is . So (a) and (b) ✓ (they say the same thing). ("pllar" in (b) is a typo for "polar".)

*Harmonic property.* Take the line through in direction : points . - On the circle:

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Question ID VK-108984