Q8 of 23 Page 230

Let (x, y) be a point on the circle with the line joining (0, 1) and (2, 3) as diameter. Prove that x2 + y2 – 2x – 4y + 3 = 0. Find the coordinates of the points where this circle cuts the x axis.

Two diametrically Opposite points are (0,1),(2,3)


Equation of circle for two Diametrically Opposite points:


(x - 0)(x - 2) + (y - 1)(y - 3) = 0


⇒ x2 - 2x + y2 - 4y + 3 = 0


When the circle cuts the x axis the y coordinate is 0


⇒ x2 - 2x + 3 = 0


Discriminant = ( - 2)2 - 4 × 1 × 3


Discriminant = - 8


Since Discriminant is negative so the roots are imaginary


Hence the circle doesn’t cut the x - axis at any point.


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