Question

. The centre of a circle is (2a, a -7). Find the value of a if the circle passes through the point (11,-9)
and has diameter 10√2 units.

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Answer 1

$\small\bold\green{hope \: it \: helps}$

Answer 2

Step-by-step explanation:

14. If the centre of circle is (2a, a – 7) then find the values of a if he circle passes through the point (11, –9) and has diameter units.

Sol. Let C(2a, a – 7) be the centre of the circle and it passes through the point P(11, –9).

∴ PQ =

⇒ CP =

⇒ CP2 = = 50

⇒ (2a – 11)2 + (a – 7 + 9)2 = 50

⇒ (2a)2 + (11)2 – 2(2a) (11) + (a + 2)2 = 50

⇒ 4a2 + 121 – 44a + (a)2 + (2)2 + 2(a)(2) = 50

⇒ 5a2 – 40a + 125 = 50

⇒ a2 – 8a + 25 = 10

⇒ a2 – 8a + 25 – 10 = 0

⇒ a2 – 8a + 15 = 0

⇒ a2 – 5a – 3a + 15 = 0

⇒ a(a – 5) –3(a – 5) = 0

⇒ (a – 5) (a – 3) = 0

⇒ a – 5 = 0 or a – 3 = 0

⇒ a = 5 or a = 3

Hence, the required values of a are 5 and 3.