Maths-
General
Easy

Question

The number of values of c such that st. line y = 4x + c touches the curve fraction numerator x to the power of 2 end exponent over denominator 4 end fraction plus y to the power of 2 end exponent equals 1 is

  1. 0    
  2. 1    
  3. 2    
  4. infinite.    

Hint:

Equation of ellipse =
x squared over a squared space plus y squared over b squared space equals 1

The correct answer is: 2



    Equation of ellipse = x squared over a squared space plus y squared over b squared space equals 1
    x squared over 2 squared space plus space y squared over 1 squared space equals 1, a = 2 and b = 1
    Given : straight line equation =  y = 4x + c , where m = 4
    We know that
    General equation of tangent of ellipse (y) = m x space plus-or-minus square root of a squared m squared plus b squared end root
    Substituting the values in above equation
    y = 4 x space plus-or-minus space square root of 2 squared 4 to the power of 2 space end exponent plus 1 squared end root
    y = 4 x space plus-or-minus space square root of 65
 comparing with y = 4x + c rightwards double arrow space c space equals plus-or-minus 65
    Thus, we have 2 values of c i.e. plus-or-minus 65

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