Grade 11Analytical Geometry
Tangents are drawn to the parabola y2=4x from the point (1,3). The length of chord of contact is
Tangents are drawn to the parabola y2=4x from the point (1,3). The length of chord of contact is
2 Answers
Arun
Length of tangent from a point to any curve S is = S^(1/2)Now from question,Length of tangent = (9 - 4)^(1/2) = 5^1/2
Himanshu gupta
Use the parametric form of the parabola, x=t^2,y=2t. The equation of the tangent at (t^2,2t) is found to be ty-x=t^2. If this passes throught (1,3), 3t-1=t^2 so t^2-3t+1=0 Solving gives t1=[3-sqrt(5)]/2 or t2=[3+sqrt(5)]/2. The length of the chord is given by sqrt[(t1^2-t2^2)^2+(2t1-2t2)^2] =sqrt(65).
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