Question

Find the equation of a circle , the end points of whose diametre are P(-4, 3) and Q(5, -3) .
1.  x2+ y2- y - 29 = 0 
2.  x2+ y2- x- 12y- 29 = 0 
3.  x2 + y2- x - 29 = 0 
4.  x2+ y2- x - 6y- 29 = 0 

Answer 1

Correct Answer - Option 3 :  x2 + y2- x - 29 = 0 

Concept: 

The equation of a circle with A(x₁, y₁) and B(x₂, y₂) as the end points of a diameter is given by:

(x - x₁)(x - x₂) + (y - y₁)(y - y₂) = 0  

Calculation: 

We know that equation of circle with the given end points of its diameter iiis given by , 

(x - x1)(x - x2) + (y - y1)(y - y2) = 0 

Here , x₁= -4, y₁= 3 and x₂= 5, y₂= -3 .

∴ The required equation of circle is 

 (x + 4)(x - 5) + (y - 3)(y + 3) = 0 

⇒ x² + y² - x - 29 = 0 

The correct option is 3.