Maths-
General
Easy

Question

The angle between the pair of tangents drawn to the ellipse 3x2+ 2y2 = 5 from the point (1,2) is-

  1. tan–1open parentheses fraction numerator 12 over denominator 5 end fraction close parentheses    
  2. tan–1(6square root of 5)    
  3. tan–1open parentheses fraction numerator 12 over denominator square root of 5 end fraction close parentheses    
  4. tan–1 (12square root of 5)    

hintHint:

find the equation of S by using
SS1=T2

The correct answer is: tan–1open parentheses fraction numerator 12 over denominator square root of 5 end fraction close parentheses



    Ѳ= tan-1(12/√5)
    Equation of the curve :S = 3x2+2y2-5=0
    S1= S(given point) = 3(1)2+2(2)2-5= 6
    T1= 3x+4y-5=0
    Use SS1=T2
    => 9x2-4y2-24xy+30x+40y-55=0

    Here, a=9,b=-4 , h=-12
    We know that
    tan Ѳ=2√(h2-ab)/(a+b) = 12/√5
    Ѳ= tan-1(12/√5)

    use the equation of S to find the value of theta.

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