Question

# If the centre of a circle is (2a, a-7), then the values of 'a', if the circle passes through the point (11,-9) and has diameter 10√2 units will be:

A

5 and 2

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B

5 and 3

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C

3 and 4

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D

4 and 5

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Solution

## The correct option is A 5 and 3 By given condition, Distance between the centre C(2a, a-7) and the point P(11,-9), which lie on the circle = Radius of the 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√22=5√2 Putting this value in equation (i), we get 50=(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 factorization method] ⇒a(a−5)−3(a−5)=0⇒(a−5)(a−3)=0∴a=3,5 Hence, the required values of 'a' are 5 and 3.

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