Question

Points (−1, ) (5, 7) lie on a circle with centre (2, −3). Find the values of . Hence find the
radius of the circle​

Answer 1

Answer:

The values of x=-13 or x= 7

Answer 2

Answer:

Step-by-step explanation:

Join OA and OB. …[radii of a circle

∴ OA = OB OA2 = OB2 …[Squaring both sides

⇒ (2 + 1)2 + (-3y – y)2 = (5 – 2)2 + (7 + 3y)2

⇒ 9+ (-4y)2 = 9 + (7 + 3y)2

⇒ 16y2 = 49 + 42y + 9y2

⇒ 16y2 – 9y2 – 42y – 49 = 0

⇒ 7y2 – 42y – 49 = 0

⇒ y2 – 6y – 7 = 0 …[Dividing both sides by 7

⇒ y2 – 7y + y – 7 = 0

⇒ y(y – 7) + 1(y – 7) = 0

⇒ (y – 7) (y + 1) = 0

y – 7 = 0 or y + 1 = 0

y = 7 or y = -1

(i) Taking y = 7