The coordinate of middle point of the chord cut off by the line 2x-5y+18 =0 on the circle x square + y square - 6 x + 2 y - 54 =0 are A ( 1,4 ) , B ( 2,4) c (4, 1 ) D ( 1, 1) which option is correct Share with your friends Share 11 Vijay Kumar Gupta answered this Consider the following figure in which the line intersects the given circle. Find the coordianates of points of intersection of the line and circle.From the equation of line, 2x-5y+18=0 2x=5y-18 x=5y-182 .....1 Put this value in equation of circle to get, x2+y2-6x+2y-54=0 5y-1822+y2-65y-182+2y-54=0 5y-1824+y2-35y-18+2y-54=0 25y2-180y+3244+y2-15y+54+2y-54=0 25y2-180y+3244+y2-13y=0 25y2-180y+324+4y2-52y=0 29y2-232y+324=0Use the quadratic formula to get, y=232±-2322-429324229 =232±53824-3758458 =232±1624058 =232±4101558 =23258±4581015 =4±2291015From 1, when y==4-2291015 x=54-2291015-182 =20-10291015-182 =2-102910152 =1-5291015When y==4+2291015 x=54+2291015-182 =20+10291015-182 =2+102910152 =1+5291015So the point of intersections are 1+5291015,4+2291015 and 1-5291015,4-2291015 Find the coordianates of points of intersection of the line and circle.From the equation of line, 2x-5y+18=0 2x=5y-18 x=5y-182 .....1 So the midpoint of chord is given by, = 1+5291015+1-52910152,4+2291015+4-22910152 = 22,82 = 1,4 So option A 1,4 is correct. 14 View Full Answer
