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A line y=mx +1 intersects the circle (x-3)^2+(y+2)^2=25 at the points P and Q . If the midpoint of the line segment PQ has x-coordinate -(3)/(5), then which one of the following options is correct ? |
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Answer» `6 le m LT 8` It is given that points P and Q are intersecting points of circle. `(x-3)^2+(y+2)^2=25` .....(i) Line `"" y=mx+1 "".....(ii)` And , the mid -point of PQ is A having x-coordinate `(-3)/(5)` so y-coordinate is `1-(3)/(5)m`. So, `A(-(3)/(5),1-(3)/(5)M)` From the figure, `because AC BOT PQ` `rArr` (slope of AC)x (slope of PQ)` =-1`. `rArr ((-2-1+(3)/(5m))/(3+(3)/(5)))xxm=-I` `rArr 3m^2-15m+18=0` `rArr m=2or 3`. |
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