Find the locus of the middle points of all chords of the parabola y^(2)=4ax which are drawn through the vertex.
Answer (1)
18th Feb, 2021
Hello candidate,
We can assume that one end of the chord is the vertex of parabola, which is O(0,0).
Let the mid point of the chords be M(h,k) and the other end of the chord be P(at2,2at)
Mid point of OP is- (2at2+0,22at+0)
Hence, M(2at2,at)⇒h=2at2, can be represented as equation (A).
So, k=at⇒t=ak
Substituting t in the equation (A), we get-
h=2a(ak)22h=ak2k2=2ah
Replacing h by x and k by y, we get that y^ 2=2ax is the required locus of mid point of chords.
Hope it helps!!
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