Question

# Question 14 If the centre of a circle is (2a, a-7), then find the values of a , if the circle passes through the point (11,-9) and has diameter 10√2 units.

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Solution

## By given condition, Distance between the centre C(2a , a-7) and the point P(11,-9), which lie on the circle = Radius of circle ∴Radius of circle=√(11−2a)2+(−9−a+7)2 ...(i)[∵distance between the points(x1,y1) and (x2,y2)d=√(x2−x1)2+(x2−y1)2]Given that, length of diameter =10√2∴Length of radius =Length of diameter2=10√222=5√2Put this value in Eq.(i), we get50=(11−2a)2+(2+a)2⇒50=121+4a2−44a+4+a2+4a⇒5a2−40a+75=0⇒a2−8a+15=0⇒a2−5a−3a+15=0 [by splitting the middle term]⇒a(a−5)−3(a−5)=0⇒(a−5)(a−3)=0∴a=3,5Hence, the required values of a are 5 and 3.

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