Maths-
General
Easy

Question

y2 = 4x is the equation of a parabola.
Assertion : Through (lambda comma lambda + 1), 3 normals can be drawn to the parabola, if lambda< 2
Reason : The point (lambda comma lambda + 1) lies outside the parabola for all lambda not equal to –1.

  1. If both (A) and (R) are true, and (R) is the correct explanation of (A).    
  2. If both (A) and (R) are true but (R) is not the correct explanation of (A).    
  3. If (A) is true but (R) is false.    
  4. If (A) is false but (R) is true.    

The correct answer is: If (A) is false but (R) is true.


    Let a normal be y equals m x minus 2 m minus m to the power of 3 end exponent text  through  end text left parenthesis lambda comma lambda plus 1 right parenthesis
    table row cell rightwards double arrow lambda plus 1 equals m lambda minus 2 m minus m to the power of 3 end exponent end cell row cell f left parenthesis x right parenthesis equals m to the power of 3 end exponent plus left parenthesis 2 minus lambda right parenthesis m plus lambda plus 1 equals 0 end cell row cell f to the power of ´ end exponent left parenthesis m right parenthesis equals 3 m to the power of 2 end exponent plus left parenthesis 2 minus lambda right parenthesis not equal to 0 text end text text f end text text o end text text r end text text end text lambda less than 2 end cell end table

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