find locus of middle point of normal chords of the parabola y^2=4x
find locus of middle point of normal chords of the parabola y^2=4x
sunny redu , 8 Years ago
Grade 12
Analytical Geometry> find locus of middle point of normal chor...
1 Answers
Vikas TU
Last Activity: 8 Years ago
Condition of the typical harmony anytime (at2, 2at) of the parabola is
y + tx = 2at + at3. … (1)
Condition of the harmony with mid point (x1, y1) is T = S1
or, on the other hand yy1 – 2a(x + x1) = y12 – 4ax1 or yy1 – 2ax = y12 – 2ax1. … (2)
Since conditions (1) and (2) are indistinguishable, 1/y1 = t/(- 2a) = (2at + at3)/t = 2a + ((- 2a)/y1)2
or, on the other hand - (y12)/2a + x1 = 2a + 4a3/(y12) or x1 – 2a = (y12)/2a + 4a3/(y12)
Consequently the locus of the center point (x1, y1) is x – 2a = y2/2a + 4a3/y2 .
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