The tangent at any point to the circle x2+y2=16  meets the coordinate axes at A and B. If the lines drawn parallel to axes through A and B meet at ‘P’ Then locus of ‘P’  is

Given circle is x2+y2=16C=(0,0).r=4letP(x1,y1)   be the point on locus⇒A(x1,0)  B(0,y1)∴eq. of  AB→ is xx1+yy1=1 …………….(1)Since equation (1)  touches the circler=d⇒4=11x12+1y12 ⇒1x12+1y12=14S.O.B.S⇒1x12+1y12=116∴  locus is 1x2+1y2=116