find the angle between the tangents drawn from the point (4,0) to the parabola y^2+4x=0

Question

kkbisht · Answer

We know that a line y=mx+c is tangent to the standard parabola y 2 =4ax if c =a/m therefore the line y=mx+a/m is always a tangent to the parabola y 2 =4ax. Here the equation of parabola is given as y 2 = -4x where a= -1. Hence the equation of tangent to this parabola is y=mx-1/m and it is given that this tangent passes through the point (4,0) therefore 0=4m-1/m => 4m 2 =1 =. m 2 =1/4=> m=+-½ .Therefore the two tangents can be drawn to the parabola from the point (4,0) with slopes m 1 =-1/2 amd m 2 =1/2 Therefore the angle b/w them is tan = (m 1 -m 2 )/(1+m 1 m 2 )=1/2-(-1/2)/(1-1/2.1/2) = 1/ 3/4 =4/3 => = (4/3) kkbisht

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find the angle between the tangents drawn from the point (4,0) to the parabola y^2+4x=0

find the angle between the tangents drawn from the point (4,0) to the parabola y^2+4x=0

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