Q. 34.2( 140 Votes )

Find the centre of a circle passing through the points (6, – 6), (3, – 7) and (3, 3)

Answer :

The figure for the question is:



Let O (x, y) be the centre of the circle. And let the points (6, - 6), (3, - 7), and (3, 3) be representing the points A, B,and C on the circumference of the circle

By distance formula, Distance between two points A(x1, y1) and B(x2, y2) is

AB = √((x2 - x1)2 + (y2 - y1)2)

Then, 

OA = √[(x- 6)2 + (y+ 6)2]


OB = √[(x- 3)2 + (y+ 7)2]


OC = √[(x- 3)2 + (y- 3)2]


As OA, OB and OC are radii of same circle, OA = OB


[(x - 6)2 + (y + 6)2]1/2 = [(x - 3)2 + (y + 7)2]1/2


-6x – 2y + 14 = 0


3x + y = 7 (i)


Similarly, OA = OC


[(x - 6)2 + (y + 6)2]1/2 = [(x - 3)2 + (y - 3)2]1/2


-6x + 18y + 54 = 0


-3x + 9y = -27 (ii)


On adding equation (i) and (ii), we obtain


10y = - 20


y = - 2


From equation (i), we obtain


3x - 2 = 7


3x = 9


x = 3


Therefore, the centre of the circle is (3, - 2)

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Section FormulaSection FormulaSection Formula30 mins
Champ Quiz | Previous Year NTSE QuestionsChamp Quiz | Previous Year NTSE QuestionsChamp Quiz | Previous Year NTSE QuestionsFREE Class
Measuring distance by Distance formulaMeasuring distance by Distance formulaMeasuring distance by Distance formula49 mins
Coordinate Geometry Important QuestionsCoordinate Geometry Important QuestionsCoordinate Geometry Important Questions38 mins
Champ Quiz | Distance FormulaChamp Quiz | Distance FormulaChamp Quiz | Distance Formula30 mins
Set of Questions on Section FormulaSet of Questions on Section FormulaSet of Questions on Section Formula54 mins
Imp. Qs. on Distance FormulaImp. Qs. on Distance FormulaImp. Qs. on Distance Formula68 mins
Distance Formula and Section FormulaDistance Formula and Section FormulaDistance Formula and Section Formula44 mins
Champ Quiz | Coordinate Geometry ProblemsChamp Quiz | Coordinate Geometry ProblemsChamp Quiz | Coordinate Geometry Problems38 mins
Quiz | Solving Important Questions on Section FormulaQuiz | Solving Important Questions on Section FormulaQuiz | Solving Important Questions on Section Formula54 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses