Points A(–1, y) and B(5, 7) Lie on a Circle with Centre O(2, –3y). Find the Values of y. Hence Find the Radius of the Circle. - Mathematics

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Points A(–1, y) and B(5, 7) lie on a circle with centre O(2, –3y). Find the values of y. Hence find the radius of the circle.

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A and B are the two points that lie on the circle and O is the centre of the circle.

Therefore, OA and OB are the radii of the circle.

Using the distance formula, we have:



Now, OB = OA              (Radii of the same circle)


9+(7+3y)2=9+16y^2 (squaring both the sides)



⇒y2−6y−7 =0



⇒y−7=0  or y+1=0

⇒y=7 or y=−1


When y = 7:
Radius of the circle, `OA=sqrt(9+16y^2)=sqrt(9+16×49)=sqrt(793)`

When y = −1:
Radius of the circle, `OA=sqrt(9+16y^2) =sqrt(9+16×1)=sqrt(25)=5`

Concept: Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
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2013-2014 (March) Delhi Set 2

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