TG EAPCET 2025 (Online) 3rd May Morning Shift | Circle Question 25 | Mathematics

The radius of a circle $C_1$ is thrice the radius of another circle $C_2$ and the centres of $C_1$ and $C_2$ are $(1,2)$ and $(3,-2)$ respectively. If they cut each other orthogonally and the radius of the circle $C_1$ is $3 r$, then the equation of the circle with $r$ as radius and $(1,-2)$ as centre is

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

$x^2+y^2-2 x+4 y+7=0$

$x^2+y^2-2 x+4 y-7=0$

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

TG EAPCET 2025 (Online) 2nd May Evening Shift

MCQ (Single Correct Answer)

-0

The slope of a common tangent to the circles $x^2+y^2=16$ and $(x-9)^2+y^2=16$ is

$\frac{8}{\sqrt{13}}$

$\frac{4}{\sqrt{13}}$

$\frac{\sqrt{17}}{8}$

$\frac{8}{\sqrt{17}}$

TG EAPCET 2025 (Online) 2nd May Evening Shift

MCQ (Single Correct Answer)

-0

The equation of the circle whose radius is 3 and which touches the circle $x^2+y^2-4 x-6 y-12=0$ internally at $(-1,-1)$ is

$5 x^2+5 y^2-8 x-14 y-32=0$

$x^2+y^2-12 x-14 y-28=0$

$3 x^2+3 y^2-8 x-14 y-31=0$

$x^2+y^2-5 x-7 y-14=0$

TG EAPCET 2025 (Online) 2nd May Evening Shift

MCQ (Single Correct Answer)

-0

Suppose $C_1$ and $C_2$ are two circles having no common points, then

There will be 3 common tangents to $C_1$ to $C_2$

There will be exactly two common tangents to $C_1$ and $C_2$

There will be no common tangent or there will be exactly two common tangents to $C_1$ and $C_2$

There will be no common tangents or there will be four common tangents to $C_1$ and $C_2$

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