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  • Find the point of intersection of the line x+2y-5=0 and the circle x^2+y^2=25.

Find the point of intersection of the line x+2y-5=0 and the circle x^2+y^2=25.

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The given line of the Circle are
x+2y-5=0......(i)
x^2+y^2=25.........(ii)
To find their point of intersection,we have to solve the above equations simultaneously.
From(i)x=5-2y,Substituting the value of x in (ii),we get
(5-2y)^2+y^2=25 Rightarrow 25-20y+4y^2+y^2=25
Rightarrow 5y^2-20y=0 Rightarrow y^2-4y=0
Rightarrow y(y-4)=0 Rightarrow y=0,y=4.
From (i),where y=0,x=5 and when y=4,x=-3.
Hence the given line and the circle intersect in two points and their coordinates are (5,0) and (-3,4).

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Deependra Verma

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