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If two tangents drawn from a point P to the parabola y 2 = 4x are at right angles, then the locus of P is

If two tangents drawn from a point P to the parabola y 2 = 4x are at right angles, then the locus of P is

Grade:12

3 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
9 years ago
Hello student,
We know that locus of point of intersection of perpendicular tangents of a parabola is its directrix.
for parabola y2=4x directrix is x=-1
Hence locus of p is x=-1
Thanks and regards
Shaik Aasif
askIItians faculty
Chakshu
13 Points
5 years ago
Y^2=4ax         eq(1)
Y^2=4x            eq(2)
Equating eq 1 and eq 2 ,
We get ....a=1
Also we know.....cm=a
Therefore c =1/m
Eq of line......y=mx+c....
Putting value of c we get,
Y=mx+1/m  =m^2x-ym+1 (a quadratic eq.)
Therefore,
m1m2=1/x       eq(3)
Also tangents are drawn to parabola at right angles [given]therefore,
m1m2=-1      Eq(4)
Equating eq 3 and 4 we get,
X=-1
Kushagra Madhukar
askIITians Faculty 628 Points
3 years ago
Dear student,
Please find the solution to your problem.
 
We know that locus of point of intersection of perpendicular tangents of a parabola is its directrix.
for parabola y2 = 4x directrix is x = – 1
Hence locus of p is x = – 1
 
Thanks and regards
Kushagra

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