﻿ A circle has radius 3 units and its centre lies on the line y = x – 1. Find the equation of the circle if it passes through (7, 3). : Kaysons Education

# A Circle Has Radius 3 Units And Its Centre Lies On The Line y = x – 1. Find The Equation Of The Circle If It Passes Through (7, 3).

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## Question

### Solution

Correct option is

x2 + y2 – 14x – 12y + 76 = 0 & x2 + y2 – 8x – 6y + 16 = 0

Let the centre of the circle be (hk). since the centre lies on y = x – 1, we get

k = h – 1                  …(1)

Since the circle passes through the point (7, 3), therefore the distance of the centre from this point is the radius r of the circle. we have

… from (1)

⇒                           h2 – 11h + 28 = 0

or                           (h – 7) (h – 4) = 0

or                           h = 7 and h = 4

from h = 7, we get k = 6 from (1)

and for h = 4, we get k = 3 from (1).

Hence there are two circles which satisfy the given conditions. They are

(x – 7)2 + (y – 6)2 = 9      or    x2 + y2 – 14x – 12y + 76 = 0

and   (x – 4)2 + (y – 3)2 = 9      or    x2 + y2 – 8x – 6y + 16 = 0.

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