TG EAPCET 2024 (Online) 9th May Evening Shift | Circle Question 3 | Mathematics

The pole of the line $x-5 y-7=0$ with respect to the circle $S \equiv x^2+y^2-2 x+4 y+1=0$ is $P(a, b)$. If $C$ is the centre of the circle $S=0$, then $P C=$

$\sqrt{a+b-1}$

$\sqrt{a^2+b^2-1}$

$\sqrt{a^3+b^3-1}$

$3 a b$

TG EAPCET 2024 (Online) 9th May Evening Shift

MCQ (Single Correct Answer)

-0

The equation of the pair of transverse common tangents drawn to the circles $x^2+y^2+2 x+2 y+1=0$ and $x^2+y^2-2 x-2 y+1=0$ is

$x^2-y^2=0$

$x y=0$

$x^2-y^2+2 x+1=0$

$x^2-y^2-2 y-1=0$

TG EAPCET 2024 (Online) 9th May Evening Shift

MCQ (Single Correct Answer)

-0

If a circle passing through the point $(1,1)$ cuts the circles $x^2+y^2+4 x-5=0$ and $x^2+y^2-4 y+3=0$ orthogonally, then the centre of that circle is

$\left(\frac{3}{4}, \frac{5}{4}\right)$

$\left(\frac{3}{2}, \frac{5}{2}\right)$

$\left(-\frac{3}{2},-\frac{5}{2}\right)$

$\left(-\frac{3}{4},-\frac{5}{2}\right)$

TG EAPCET 2024 (Online) 9th May Evening Shift

MCQ (Single Correct Answer)

-0

Length of the common chord of the circles $x^2+y^2-6 x+5=0$ and $x^2+y^2+4 y-5=0$ is

$\sqrt{13}$

$\frac{12}{\sqrt{13}}$

$\frac{6}{\sqrt{13}}$

$2 \sqrt{13}$

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