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True/False: Circle | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

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Q.1. No tangent can be drawn from the point (5/2, 1) to the circumcircle of the triangle with vertices (1, True/False: Circle | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE) (1,- True/False: Circle | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE) , (3,-True/False: Circle | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE) . (1985 - 1 Mark) 

Ans. T

Sol. The circle passes through the points True/False: Circle | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE and True/False: Circle | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
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) + True/False: Circle | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
⇒ x2 + y2 – 4x = 0 … (1)
Let us check the position of pt (5/2, 1) with. respect  to the circle (1),
we get  True/False: Circle | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

∴ 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.

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