Question

16. Find the centre, radius and the equation of the circle drawn on the line segment joining
the points (-1, 2) and (3, -4) as diameter.​

Answer 1

hope the answer helps you::)

Answer 2

We have to find the centre , radius and the equation of the circle drawn on the line segment joining the points (-1, 2) and (3,-4) as diameter.

solution : centre is the midpoint of diameter.

so using midpoint section formula,

centre of circle = [(-1 + 3)/2, (2 - 4)/2 ] = (1, -1)

radius of circle = length of diameter/2

= √{(-1 - 3)² + (2 + 4)²}/2

= √{(-4)² + (6)²}/2

= √(16 + 36)/2

= √13

equation of circle is given by,

(x - a)² + (y - b)² = r²

where (a, b) is centre of circle and r is the radius of the circle.

so, equation of circle is (x - 1)² + (y + 1)² = (√15)²

⇒x² - 2x + 1 + y² + 2y + 1 = 13

⇒x² + y² - 2x + 2y - 11 = 0