Please solve this : Share with your friends Share 0 Bakul Biswas answered this Dear Student, Consider the following diagram which depicts the given condition. The slope of the line OP passing through O0,0 and P1,2 is, 2-01-0=2So the slope of the tangent line at P perpendicular to OP is -12Now equation of tangent line at P is given by, y-2=-12x-1 y-2=-12x+12 y=-12x+12+2 y=-12x+52Find the point of intersection of this tangent line and the second circle x2+y2=9Substitute y=-12x+52 in x2+y2=9 to get, x2+-12x+522=9 x2+14x2+254-52x=9 4 x2+ x2+25-10x4=9 5 x2-10x+25=36 5 x2-10x-11=0Solve using quadratic formula to get, x=5+455, 5-455When x=5+455, then y=-125+455+52=10-255When x=5-455, then y=-125-455+52=10+255So the coordinates of points A and B are5-455,10+255 and 5+455,10-255 respectively.To find the coordinates of point C, first find the equation of tangents at point A and BThe point of intersection of these tangent lines gives the point C.The slope of the tangent at A is, -1slope of OA= -110+2555-455=-5-4510+25=-9-558So equation of tangent line at A is, y-10+255=-9-558x-5-455 y-10+255=-9-558x+9-555-4540 y-10+255=-9-558x+145-61540This further implies that, y=-9-558x+145-61540+10+255 y=-9-558x+225-45540 y=55-98x+45-958 .....1 In a similar way, find the equation of tangent at point B to get, y=-55-98x+45+958 .....2 Solve 1 and 2 to get, x=95=1.8and y=185=3.6Thus the coordinate of point C is 1.8,3.6 option(D) is correct. Hope this information will clear your doubts about topic. If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible. Regards 0 View Full Answer
