+y2=1.....(ii) Put value of y from Eqs. (i) into (ii), we get
x2
4
+(4x+c)2=1 ⇒x2+4(4x+c)2=4 ⇒x2+4(16x2+8cx+c2)=4 ⇒x2+64x2+32cx+4c2=4 ⇒65x2+32cx+4(c2−1)=0 since, given line is a tangent to the ellipse. ∴ Discriminant =0 ⇒(32c)2−4×65×4(c2−1)=0 ⇒1024c2−1040(c2−1)=0 ⇒16c2=1040 ⇒c2=65 ⇒c=±√65