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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 ?
tan45 = |3 – m|/|1 + 3m| = 1/root2solvinf for m we get, m = ½.TANGENT OF parabola = > 2ydy/dx = 8dy/dx = 4/y1 |let x1 and y1 be the point of contact] m = 4/y1 = ½y1 = 8.x1 = 64/8 = 8the eqn. from point of contact (8,8) and slope = ½.(y – 8) = 0.5(x -8)y = x/2 + 4 is the required eqn.
Tan45=|3-m|/|1+3m|From this m=1/2,-2As we know that eqn of tangent of parabola is given by y=mx+a/m. .......1By putting value of m in eqn m We get x-2y+8=0 and 2x+y=0
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