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A tangent to the parabola y^2=8x makes an angle 45° with the straight line y=3x +5. find eqn of tangent abd its point of contact ?

A tangent to the parabola y^2=8x makes an angle 45° with the straight line y=3x +5. find eqn of tangent abd its point of contact ?

Grade:11

2 Answers

Vikas TU
14149 Points
5 years ago
tan45 = |3 – m|/|1 + 3m| = 1/root2
solvinf for m we get, m = ½.
TANGENT OF parabola = > 2ydy/dx = 8
dy/dx = 4/y1 |let x1 and y1 be the point of contact]
 
m = 4/y1 = ½
y1 = 8.
x1 = 64/8 = 8
the eqn. from point of contact (8,8) and slope = ½.
(y – 8) = 0.5(x -8)
y  = x/2  + 4 is the required eqn.
Shivank Shekhar
14 Points
3 years ago
Tan45=|3-m|/|1+3m|
From this m=1/2,-2
As we know that eqn of tangent of parabola is given by y=mx+a/m.        .......1
By putting value of m in eqn m 
We get x-2y+8=0 and 2x+y=0
 

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