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no. of circles that touches a given parabola and one of its fixed focal chords at focus is?

no. of circles that touches a given parabola and one of its fixed focal chords at focus is?

Grade:12th pass

1 Answers

RISHIKESH VERMA
26 Points
3 years ago
Let the parabola is
2
y 4x. 
The equations
     
2
2 2 2
x t y 2t 2 x yt t 0        
and
   
2 2
x 1 y 2 mx y m 0       
should represent the same circle touching mx –
y – m = 0 at (1, 0) and the parabola at (t2
, 2t). Eliminating  and , we get mt3
– 3t2
3mt + 1 = 0 will give three values of t for any given m.

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