Most Important Selected Qs for JEE AdvancedMathematicsParabola

Consider a parabola y^2= x and a point (- 4 , 0 ) then midpoint of centres of the circles touching the tangents from given point and its chord of contact is

Options

A2
B4
C3 2
Dnone of these

Correct answer

D. none of these

Step-by-step solution

(- 4 , 0 ) lies on directrix and centre be (x₁, 0 ) . Equation of one of the tangent is x+y+ 4 =0 and chord is x- 4 =0 , centre is (x₁, 0 ) |x₁+ 4 | 2 = |x₁- 4 | 1 x₁^2+ ^2 16 + x 2 =2 x₁^2+ ^2 8 - xx₁^2- 3 x 2 + ^2 16 =0 x₁+x₂= 3 2 Midpoint ( 3 4 , 0 )

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