Let T be the line passing through the points P - 2 , 7 and Q 2 , - 5 . Let F 1 be the set of all pairs of circles S 1 , S 2 such that T is tangents to S 1 at P and tangent to S 2 at Q , and also such that S 1 and S 2 touch each other at a point, say, M . Let E 1 be the set representing the locus of M as the pair S 1 , S 2 varies in F 1 . Let the set of all straight line segments joining a pair of distinct points of E 1 and passing through the point R 1,1 be F 2 . Let E 2 be the set of the mid-points of the line segments in the set F 2 . Then, which of the following statement(s) is (are) TRUE?

The point 0 , 3 2 does NOT lie in E 1

E M B I B E

Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-2>Q 51

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Curves $a x^{2} + 2 h x y + b y^{2} - 2 g x - 2 f y + c = 0$ and $a^{'} x^{2} - 2 h x y + (a^{'} + a - b) y^{2} - 2 g^{'} x - 2 f^{'} y + c = 0$ intersect at four concyclic points $A, B, C$ and $D$ . If $P$ be the point $(\frac{g^{'} + g}{a^{'} + a}, \frac{f^{'} + f}{a^{'} + a})$ , then which of the following is/are true $?$

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Important Questions on Circle

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Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-2>Q 54

Set of values of

m

for which a chord of slope

m

of the circle

x^{2} + y^{2} = 4

touches parabola

y^{2} = 4 x

, may lie in interval

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Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-3>Q 1

Three distinct points

A, B

and

C

are given in the

2

-dimensional coordinate plane such that the ratio of the distance of any one of them from the point

(1, 0)

to the distance from the point

(- 1, 0)

is equal to

\frac{1}{3}

. Then the circumcentre of the triangle

A B C

is at the point

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Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-3>Q 2

Tangents drawn from the point $P (1, 8)$ to the circle $x^{2} + y^{2} - 6 x - 4 y - 11 = 0$ touch the circle at points $A$ and $B$ . The equation of the circumcircle of triangle $P A B$ is

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Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-3>Q 5

The circle passing through the point

(- 1, 0)

and touching the

Y

-axis at

(0, 2)

also passes through the point

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Alpha Question Bank for Engineering: Mathematics>Chapter 16 - Circle>Exercise-3>Q 6

The straight line $2 x - 3 y = 1$ divides the circular region $x^{2} + y^{2} \leq 6$ into two parts. If $S = \{(2, \frac{3}{4}), (\frac{5}{2}, \frac{3}{4}), (\frac{1}{4}, - \frac{1}{4}), (\frac{1}{8}, \frac{1}{4})\}$ , then the number of point(s) in $S$ lying inside the smaller part is ________.