If the center 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 units.

Using the given condition;

As distance between two points (x_{1}, y_{1}) and (x_{2}, y_{2});

d =

So,

Distance between the centre C (2a, a – 7) and the point P (11, - 9), which lie on the circle = Radius of circle.

…….(i)

Given that,

Length of diameter =

By putting this value in Eq. (i),

We get;

By squaring both sides,

We get;

50 = (11 – 2a)^{2} + (2 + a)^{2}

→ 50 = 121 + 4a^{2} – 44a + 4 + a^{2} + 4a

→ 5a^{2} – 40a + 75 = 0

→ a^{2} – 8a + 15 = 0

→ a^{2} – 5a – 3a + 15 = 0

By factorization method;

a(a – 5) – 3(a – 5) = 0

(a – 5)(a – 3) = 0

a = 3, 5

Hence, the values of a are 5 and 3.

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