JEE Advanced (True/False): Circle
Q.1. No tangent can be drawn from the point (5/2, 1) to the circumcircle of the triangle with vertices (1, 
) (1,- ) , (3,-) . (1985 - 1 Mark)
Ans. T
Sol. The circle passes through the points 
and 
Here line AB is parallel to y-axis and BC is parallel to x-axis, there ∠ABC = 90°
∴ AC is a diameter of circle.
∴ Eq. of circle is
(x - 1) (x - 3) + 
⇒ x2 + y2 - 4x = 0 ... (1)
Let us check the position of pt (5/2, 1) with. respect to the circle (1),
we get 
∴ Point lies inside the circle.
∴ No tangent can be drawn to the given circle from point (5/2, 1).
∴ Given statement is true.
Q.2. The line x + 3y = 0 is a diameter of the circle x2 + y2 - 6x + 2y = 0. (1989 - 1 Mark)
Ans. T
Sol. The centre of the circle x2 + y2 - 6x + 2y = 0 is (3, - 1)
which lies on the line x + 3y = 0
∴ The statement is true.
