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Most Important Selected Qs for JEE AdvancedMathematicsParabola

A circle 'S' is described on the focal chord of the parabola y^2=4 x as diameter. If the focal chord is inclined at an angle of 45^ with axis of x, then which of the following is/are true

Options

  1. Aradius of the circle is 4
  2. Bcentre of the circle is (3,2)
  3. Cthe line x+1=0 touches the circle
  4. Dthe circle x^2+y^2+2 x-6 y+3=0 is orthogonal to ' S '

Correct answer

C. the line x+1=0 touches the circle

Step-by-step solution

Circle on PQ as diameter aligned & (x-t₁^2 ) (x-t₂^2 )+ (y-2 t₁ ) (y-2 t₂ )=0 & x^2+y^2- (t₁^2+t₂^2 ) x-2 (t₁+t₂ ) y+t₁^2 t₂^2+4 t₁ t₂=0 aligned Put t₁+t₂ 2 =1 and t₁ t₂=-1 Hence equation of circle become x^2+y^2-6 x-4 y-3=0 ...(1) With centre (3,2) and radius 4 Equation (1) is not orthogonal to x^2+y^2+2 x-6 y+3=0

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