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The condition that lx+my+c=0 maybe a normal to the parabola with related example

The condition that lx+my+c=0 maybe a normal to the parabola with related example
 

Grade:12

1 Answers

Arun
25750 Points
5 years ago
the condition of the given parabola is y2=4ax 
the condition of the ordinary to the given parabola is y+tx=2at+at3 
i.e. tx+y−(2at+at3)=0 ........(1) 
the condition (1) and the given condition of the ordinary lx+my+n=0 ...........(2) speak to a similar line: 
subsequently 
t/l=1/m=−(2at+at3)/n 
t/l=1/m⇒t=l/m ........(3) 
furthermore, 1/m=−(2at+at3)n 
−n/m=2at+at3 
−n/m=2a.(l/m)+a.(l/m)3 [ substituting the estimation of t from eq(3)] 
−n/m=2a.l/m+a.(l/m)3 
⇒−n.m2=2a.lm2+a.l3 
⇒a.l3+2alm2+nm2=0 

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