Maths-
General
Easy

Question

Statement- (1) : PQ is a focal chord of a parabola. Then the tangent at P to the parabola is parallel to the normal at Q.
Statement- (2) : If P(t1) and Q(t2) are the ends of a focal chord of the parabola y2 = 4ax, then t1t2 = –1.

  1. Both S1 & S2 are correct & S2 is correct explanation of S1    
  2. Both S1 & S2 are correct but S2 is not correct explanation of S1    
  3. S1 is correct S2 is wrong    
  4. S1 is wrong S2 is correct    

hintHint:

properties of tangent and normal of a parabola.

The correct answer is: Both S1 & S2 are correct & S2 is correct explanation of S1



    Both S1 & S2 are correct & S2 is correct explanation of S1

    equation of tangent at P : t1y = x+at2
    equation of normal at Q : y+ xt2 = 2at2 + at23
    the slopes at P and Q are 1/t1 and -t2 respectively

    slopes at the two extremeties of a focal chord are : (t,-1/t)
    this property is used to explain the behaviour of tangents and normals at the respective points.

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