TS EAMCET 2020 (Online) 14th September Morning Shift | Circle Question 155 | Mathematics

In the List-I each item contains equations of two circles, List-II contains the number of common tangents for each pair of circles given in List-I. Match the items of List-I with those of the items of List-II

$$ \text { List-I } $$		$$ \text { List-II } $$
A.	$$ \begin{aligned} & x^2+y^2+2 x+8 y-23=0 \\ & x^2+y^2-4 x-10 y+19=0 \end{aligned} $$	I.	0
B.	$$ \begin{aligned} & x^2+y^2=1 \\ & x^2+y^2-2 x-6 y+6=0 \end{aligned} $$	II.	1
C.	$$ \begin{aligned} & x^2+y^2-8 x+2 y=0 \\ & x^2+y^2-2 x-16 y+25=0 \end{aligned} $$	III.	2
D.	$$ \begin{aligned} & x^2+y^2=4 \\ & x^2+y^2-2 x=0 \end{aligned} $$	IV.	3
		V.	4

$$ \text { The correct match is } $$

A	B	C	D
V	I	III	II

A	B	C	D
IV	I	III	II

A	B	C	D
IV	V	III	II

A	B	C	D
III	IV	I	IV

TS EAMCET 2020 (Online) 14th September Morning Shift

MCQ (Single Correct Answer)

-0

$\left(0, \frac{3}{4}\right)$ is the radical centre of the circles $S_1: x^2+y^2-2 x+6 y=0, S_2: x^2+y^2+2 g x-2 y+6=0$ and $S_3: x^2+y^2-12 x+2 f y+3=0$. If $S_2$ and $S_3$ intersect orthogonally, then $(g, f)=$

$\left(\frac{-11}{12}, 1\right)$

$\left(1, \frac{-21}{2}\right)$

$\left(0, \frac{-9}{2}\right)$

$\left(-1, \frac{-7}{12}\right)$

TS EAMCET 2020 (Online) 14th September Morning Shift

MCQ (Single Correct Answer)

-0

For the circles $(x-a)^2+y^2=a^2$ and $x^2+(y-a)^2=a^2$, where $a>0$, which one of the following is not true?

mid-point of the common chord is $\left(\frac{a}{2}, \frac{a}{2}\right)$

length of the common chord is $(\sqrt{2} a)$

the circles intersect at $(0,0)$ and $(a, a)$

common chord is at a distance of $(\sqrt{2} a)$ units from the centres of given circles

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