Maths-
General
Easy

Question

If the line x plus y plus k equals 0 is a tangent to the parabola x to the power of 2 end exponent equals 4 y then k=

  1. 1    
  2. 2    
  3. 3    
  4. 4    

Hint:

The parabola equation is simplest if the vertex is at the origin and the axis of symmetry is along the x-axis and y-axis.
x squared space equals space 4 a y
In parabola a line to be a tangent to parabola, condition is c space equals space a over m

The correct answer is: 1


     Given Parabola : x to the power of 2 end exponent equals 4 y
    Comparing with standard equation of parabola x squared space equals space 4 a y
    4ay = 4y
    a = 1
    Given line : x plus y plus k equals 0
    Comparing with standard equation of line y space equals space m x space plus space c

    m = 1 and c = k
    In parabola a line to be a tangent to parabola, condition is c space equals space a over m
    Substituting these values
    k space equals space 1 over 1
    Thus, If the line x plus y plus k equals 0 is a tangent to the parabola x to the power of 2 end exponent equals 4 y then k= 1

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