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Most Important Selected Qs for JEE AdvancedMathematicsCircle

Paragraph: A rectangle P Q R S is inscribed in a circle C with centre O and a diameter along the line 2 y-4 x=9 . P and Q are the points (-8,-2) and (4,-2) respectively. Let a circle C₁ be drawn taken RS as the diameter. On the basis of above information, answer the following : Question: A line through (7,5) at maximum distance from point O will have slope equal to -

Options

  1. A1
  2. B1 2
  3. C-1
  4. D-2

Correct answer

D. -2

Step-by-step solution

Let O ( h , k ) be the centre of the circle C aligned & 2 k -4 ~h =9 . . . (i) & Also OP = OQ = Radius of the circle & OP ^2= OQ ^2 or h +8= ( h -4) & h +8=- h +4 ~h =-2 aligned Putting in (i), k = 1 2 array ll & Radius = OP = 13 2 & P R=13 array aligned & In PQR , PR ^2= PQ ^2+ QR ^2 & 169=144+ QR ^2 QR =5 aligned Also co-ordinates of R & ~S are respectively (4,3) &(-8,3) The line through (7,5) at maximum distance from centre O of circle C will be the line perpendicular to line joining (7,5) & point O . slope of r

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