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=14√73 D) c=√57 Answer: Option CExplanation: if the line y=mx+c isa normal to the ellipse x2a2+y2b2=1 , then c2=m2(a2−b2)2a2+b2m2 [Here , m=2, a2 =9 , and b2 =16] =22(9−16)29+16×(2)2 =4×499+64=4×4973=19673 ∴ c=14√73