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1)

If the line y=2x+c  is a  normal to the ellipse   x29+y216=1   , then 


A) c=23

B) c=735

C) c=1473

D) c=57

Answer:

Option C

Explanation:

 if the line y=mx+c isa normal to the ellipse   x2a2+y2b2=1 , then

 c2=m2(a2b2)2a2+b2m2

 [Here , m=2, a2 =9 , and  b2 =16]

=22(916)29+16×(2)2

 =4×499+64=4×4973=19673

   c=1473