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Question

# Find the point of Intersection of the circle x2+y2=4 with line passing through A(1,0) and B(3,4).

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Solution

## Circle : x2+y2=4⇒ Centre =(0,0) Radius 2 unitsline passing through: A(1,0) and B(3,4)Equation of line passing through two given points y−y1=y2−y1x2−x1(x−x1)(x1,y1)=(1,0)(x2,y2)=(3,4)⇒y−0=4−03−1(x−x1)⇒y=2(x−1) Equation of given lineAt the point of intersection both line and circle will passing through the same point ∴ Putting y=2(x−1) in the equation of the circle.x2+[2(x−1)]2=4⇒x2+4(x2+1−2x)=4⇒x2+4x2+4−8x=4⇒5x2−8x=0⇒x(5x−8)=0⇒x=0 or x=8/5Putting x=0 and x=8/5 in the equation of the line to get respective values of yFor x=0,y=2(0−1)=−2 ]⇒ Point of intersection are (0,−2) and (8/5,6/5)For x=8/5,y=2(8/5−1)=6/5Points of intersection : (0,−2) and (8/5,6/5)

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