TS EAMCET 2020 (Online) 14th September Morning Shift | Circle Question 157 | Mathematics

$\left(0, \frac{3}{4}\right)$ 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

TS EAMCET 2020 (Online) 11th September Evening Shift

MCQ (Single Correct Answer)

-0

Let $a=1+i$ and $z=x+i y$. If the curve $z \bar{z}+a z+\bar{a} \bar{z}-4=0$ is cut by the straight line $(z+\bar{z})-i(z-\bar{z})+2=0$ at two points $A$ and $B$, then the equation of the circle passing through the origin, $A$ and $B$ is

$x^2+y^2+3 x-4 y=0$

$x^2+y^2+x+y=0$

$x^2+y^2+6 x+2 y=0$

$x^2+y^2-7 x-12 y=0$

TS EAMCET 2020 (Online) 11th September Evening Shift

MCQ (Single Correct Answer)

-0

A point $P$ moves so that distance from $(0,2)$ to $P$ is $\frac{1}{\sqrt{2}}$ times the distance of $P$ from $(-1,0)$. Then the locus of the point is

a circle with centre at $(1,4)$ and radius $\sqrt{10}$

a parabola with focus at $(1,4)$ and length of latus rectum 10

an ellipse with centre at $(-1,-4)$ and length of the major axis $\sqrt{10}$

a hyperbola with centre at $(-1,-4)$ and length of the transverse axis 10

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