In Sahakar Nagar, few enthusiastic teenagers, who are fond of outdoor games and are aware of the importance of fitness, are unable to play on the ground in their neighbourhood. They are busy with their online classes, assignments and other homework the whole day and in the evening as now a days it gets dark early, they are unable to play in the dark. They have written an application to the local municipal authority requesting to make the arrangement of light on the ground so that many others will also get benefit of the same. Parents also have supported this and after the meeting with the MLA, it is decided that a pole for the flood light is to be erected at a point on the boundary of that circular ground of diameter 13 metres in such a way that the difference of its distance from two diametrically opposite fixed gates A and B on the boundary is 7 metres. 4
i Draw the labelled diagram of circular ground depicting the above situation.
ii Is it possible to erect the pole as per the conditions given?
iii If yes, frame a quadratic equation for the given situation assuming a suitable variable.
iv Solve the equation and determine the necessary distance.
v State the condition for the quadratic equation under which, real roots are not possible.
Answers
In Sahakar Nagar, few enthusiastic teenagers, who are fond of outdoor games and are aware of the importance of fitness, are unable to play on the ground in their neighbourhood. They are busy with their online classes, assignments and other homework the whole day and in the evening as now a days it gets dark early, they are unable to play in the dark. They have written an application to the local municipal authority requesting to make the arrangement of light on the ground so that many others will also get benefit of the same. Parents also have supported this and after the meeting with the MLA, it is decided that a pole for the flood light is to be erected at a point on the boundary of that circular ground of diameter 13 metres in such a way that the difference of its distance from two diametrically opposite fixed gates A and B on the boundary is 7 metres. 4
i Draw the labelled diagram of circular ground depicting the above situation.
ii Is it possible to erect the pole as per the conditions given?
iii If yes, frame a quadratic equation for the given situation assuming a suitable variable.
iv Solve the equation and determine the necessary distance.
v State the condition for the quadratic equation under which, real roots are not possible.