Question

# The radius of the circle with centre at the origin is 10 units. Write the coordinates of the point where the circle intersects the axes. Find the distances between any two of such points.

A
Coordinates=(10,0)(10,0)(0,10)(0,10), Distance=20,102units
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B
Coordinates=(10,0)(10,0)(0,10)(0,10) Distance=10,102units
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C
Coordinates=(10,0)(10,0)(0,10)(0,10),0 Distance=202or102units
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D
none
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Solution

## The correct option is A Co−ordinates=(10,0)(−10,0)(0,10)(0,−10), Distance=20,10√2unitsThe equation of circle with radius 10 and centre (0,0)x2+y2=102 .................eq(i)and equation of axes are x=0 and y=0 .............eq(ii)putting x=0 in eq(i) we get⇒y2=100⇒y=±10thus we get two coordinates A(0,10) and C(0,−10)putting y=0 in eq(i) we get⇒x2=100⇒x=±10thus we get two coordinates B(10,0) and D(−10,0)Calculation of distances between any two adjacent pointsAB=√(0−10)2+(10−0)2=√200=10√2unitsAB=BC=CD=DA=10√2unitsand,Calculation of distances between any two opposite pointsBD=√(10−(−10))2+(0−0)2=20unitsAC=BD=20units

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