A point moves such that the sum of the squares of its distances from two intersecting straight lines is constant.
a)identify which conic it is
b)find the eccentricity of the conic in terms of the angle between the straight lines
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3 Answers
1i just missed out that the anglee between d 2 straight lines is θ
and the answr is in terms of θ
62because we just have to identify the curves.. we chose the lines to be the x axis and the line y-mx=0 (where m = tan θ)
now we chose a point h,k
the sum of the squares of the distance is k2+(k-mh)2/(1+m2) = c
Which clearly says the this is a ellipse...
We know the value of a2 and b2 .. we can find the eccentricity.. [1]
Can you try to complete the proof from here?