The given equation of the circle is x2+y2+6x+4y−12=0 The centre (-3,-2) The radius =√9+4+12=5
The shortest distance between point P and the circle isAP=OP−OA AP=√(−3−2)2+(−2+14)2−5 =13 AP=8 Length of tangent from point P is =√22+(−14)2+6.2+4(−14)−12 =12 The required length is =√8+12=2√5