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Question

The focus of the parabola left parenthesis y minus 2 right parenthesis to the power of 2 end exponent equals 20 left parenthesis x plus 3 right parenthesis text  is end text

  1. (3, −2)    
  2. (2, −3)    
  3. (2, 2)    
  4. (3, 3)    

The correct answer is: (2, 2)


    We know that the standard equation of a parabola is
    left parenthesis y minus beta right parenthesis to the power of 2 end exponent equals 4 a left parenthesis x minus alpha right parenthesis On comparing the given equation with the standard equation, we get the vertex as
    left parenthesis alpha comma beta right parenthesis equals left parenthesis negative 32 right parenthesis and a = 5. Therefore, the focus of the parabola is left parenthesis alpha plus a comma beta right parenthesis = (2, 2).

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