TG EAMCET 4 May 2025 Shift 2 Paper

Let the slope of common tangent be m.
Equation of tangent of slope m to
‌

x2

16

−‌

y2

9

=1‌ is ‌y=mx±√16m2−9
Equation of tangent of slope m to
‌x2+y2=16‌ is ‌y=mx±4√1+m2
‌⇒16m2−9=16+16m2
‌⇒0m2+0m−25=0
⇒ Both roots are at infinity
⇒ Slope of common tangent is undefined which is parallel to Y-axis. So, number of common tangent is 2 .