Question 175 of 219MediumMCQ
The number of common tangents to the circles x2+y2−4x−6x−12=0 and x2+y2+6x+18y+26=0, is : Solutions · 1
Official solution
\[{x^2} + {y^2} - 4x - 6y - 12 = 0\,\,\,\,\,\,\,\,\,\,\,\,...\left( i \right)\]
Center, \[{c_1} = \left( {2,\,3} \right)\] and Radius, r1=5 units
\[{x^2} + {y^2} + 6x + 18y + 26 = 0\,\,\,\,\,\,\,\,\,\,\,...\left( {ii} \right)\]
Center, \[{c_2} = \left( { - 3, - 9} \right)\] and Radius, r2=8 units
\[{C_1}{C_2} = \sqrt {{{\left( {2 + 3} \right)}^2} + {{\left( {3 + 9} \right)}^2}} = 13\,\,\] units
r1+r2=5+8=13
\[\therefore\] C1C2=r1+r2
Therefore there are three common tangents. Answer the question to unlock