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The -equation (x-x1)(x-x2)+(y-y1)(y-y2)=...

`The -equation (x-x_1)(x-x_2)+(y-y_1)(y-y_2)=0` Represents a circle whose centre is

A

`((x_1+x_2)/(3),(y_1+y_2)/(3))`

B

`((y_1+x_2)/(2),(x_1+y_2)/(2))`

C

`((x_1+x_2)/(2),(y_1+y_2)/(2))`

D

`((y_1+x_2)/(4),(x_1+y_2)/(4))`

Text Solution

Verified by Experts

The correct Answer is:
C
Given, `(x-x_1)(x-x_2)+(y-y_1)(y-y_2)=0`,whose extremities of diameter are `(x_1,y_1)` and `(x_2,y_2)`. Hence, coordinates of centre of cricle is `((x_1+x_2)/(2),(y_1+y_2)/(2)).`
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Knowledge Check

  • Statement-1: The equation x^(2)-y^(2)-4x-4y=0 represents a circle with centre (2, 2) passing through the origin. Statement-2: The equation x^(2)+y^(2)+4x+6y+13=0 represents a point.

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    Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1.
    B
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    C
    Statement-1 is True, Statement-2 is False.
    D
    Statement-1 is False, Statement-2 is True.

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    Two mutually perpendicular lines
    B
    two parallel lines
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    Two lines
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    a circle

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