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p(x y) and q(x" y' )'are two points on the parabola y2=4ax and r(x'''y''' ) is a point on the arc PQ such that the tangent at R to the parabola is parallel to the chord PQ show that x''' is a.m of x and x'

p(x y) and q(x" y' )'are two points on the parabola y2=4ax and r(x'''y''' ) is a point on the arc PQ such that the tangent at R to the parabola is parallel to the chord PQ show that x''' is a.m of x and x'

Grade:12

1 Answers

Aman Bansal
592 Points
10 years ago

dear pritomrit,

comparing the  slopes calculated from both the cases

1. m=(y''-y')/(x''-x')

2. and also the equation of tangent is 2yy'''=2a(x+x''')

from this equation slope is a/y

3 also using relation y2= 4ax

thus we can form e relation between x,x',x'''

thus can be solved

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