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find the angle between the tangents drawn from the point (4,0) to the parabola y^2+4x=0
We know that a line y=mx+c is tangent to the standard parabola y2=4ax if c=a/m therefore the line y=mx+a/m is always a tangent to the parabola y2=4ax. Here the equation of parabola is given as y2= -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 => 4m2=1 =. m2=1/4=> m=+-½ .Therefore the two tangents can be drawn to the parabola from the point (4,0) with slopes m1=-1/2 amd m2=1/2Therefore the angle b/w them is tan = (m1-m2)/(1+m1m2)=1/2-(-1/2)/(1-1/2.1/2) = 1/3/4 =4/3 => = (4/3) kkbisht
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