﻿ Find the equation of circle passing through the three non-collinear points (1, 1), (2, –1) and (3, 2). : Kaysons Education

# Find The Equation Of Circle Passing Through The Three Non-collinear Points (1, 1), (2, –1) And (3, 2).

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## Question

### Solution

Correct option is

x2 + y2 – 5x – y + 4 = 0

Let the equation of the circle be

x2 + y2 + 2gx + 2fy + c = 0           …(i)

Since the three given points lie on circle (1), we get

1 + 1 + 2g + 2f + c = 0    or    2g + 2f + c + 2 = 0      …(ii)

⇒    4 + 1 + 4g + 2f + c = 0   or     4g – 2f + c + 5 = 0      …(iii)

⇒   9 + 4 + 6g + 4f + c = 0    or     6g + 4f + c + 13 = 0    …(iv)

Subtracting (2) from (3) and subtracting (3) and from (4), then

2g – 4f + 3 = 0              …(v)

and          2g + 6f + 8 = 0              …(vi)

Solving (5) and (6), we get

Now from (2), –5 – 1 + c + 2 = 0

c = 4

hence from (1), equation of circle is

x2 + y2 – 5x – y + 4 = 0

#### SIMILAR QUESTIONS

Q1

Find the equation of the circle the end points of whose diameter are the centers of the circle.

x2 + y2 + 6x – 14y = 1 and x2 + y2 – 4x + 10y = 2

Q2

The sides of a square are x = 2, x = 3, y = 1, y = 2 find the equation of the circle drawn on the diagonals the square as its diameter.

Q3

The abscissas of two point A and B are the roots of the equation x2 + 2ax – b2 = 0 and their ordinate are the roots of the equation x2 + px – q2 = 0. Find the equation and the radius of the circle with AB as diameter.

Q4

Find the equation of the circle which passes through the points (4, 1), (6, 5) and has its centre on the line 4x + y = 16.

Q5

Find the equation of the circle whose diameter is the line joining the points (–4, 3) and (12, –1). Find also the intercept made by it on y axis.

Q6

Find the equation of circle which touches axis of y at a distance 4 units from the origin and cuts the intercept of 6 units from the axis of x.

Equation of circle in intercepts

Q7

Find the equation of the circle which passes through the origin and makes intercepts of length a and b on axis of x and y respectively.

Q8

A circle of radius 2 lies in the first quadrant and touches both the axes of coordinate. Find the equation of circle with centre at (6, 5) and touching the above circle externally.

Q9

A circle of radius 5 units touches the coordinates axes in 1st quadrant. If the circle makes one complete roll on x axis along positive direction of xaxis. Find the equation in new position.

Q10

Discus the position of the points (1, 2) and (6, 0) with respect to the circle.

x2 + y2 – 4x + 2y – 11 = 0