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Question

The centre of a circle is (2a,a7). Find the values of a if the circle passes through the point (11, -9) and has diameter 102 units.

A
35
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B
3
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C
5
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D
53
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Solution

The correct options are
A 35
C 5
LetthegivenpointP(x1,y1)=(11,9)lieonacirclewithcentreat

C(x2,y2)=(2a,a7)&radius=r.

ThenPC=r.......(i)

Giventhatthediameterofthecircle=102units.

r=diameter2=102units2=52units....(ii).

Again,bydistanceformula,d=(x1x2)2+(y1y2)2

PC=d=(112a)2+(9a+7)2=5a240a+125.

From(i)&(ii)weget

5a240a+125=(52)2

5a240a+75=0

(a5)(5a3)=0

a=5,35

Ansa=5,35


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