Maths-
General
Easy

Question

Find the equations of tangents to the ellipse 9x2 + 16y2 = 144 which pass through the point (2,3).

  1. y = 3 and y = –x + 5    
  2. y = 5 and y = –x + 3    
  3. y = 3 and y = x – 5    
  4. None of these    

hintHint:

substitute the values of x and y to find the values of m and substitute that into the equation.

The correct answer is: y = 3 and y = –x + 5



    y=3 and x+y=5
    Equation of ellipse : 9x2+16y2=144
    Or,
    x2/16+y2/9=1
    equation of ellipse is given by :
    y= m+ √(a2m2+b2)
    substituting the values of x and y, we get
    12m2+12=0
    => m2+m=0
    Or, m=0,-1
    Substituting the 2 values of m into the equation, we get
    y=3 and x+y=5

    equation of tangent of an ellipse is given by :
    y= m+ √(a2m2+b2)
    this is used to find the values of m.

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