TG EAPCET 2025 (Online) 2nd May Morning Shift | Straight Lines and Pair of Straight Lines Question 29 | Mathematics

If a line $L$ passing through a point $A(2,3)$ intersects another line $4 x-3 y-19=0$ at the point $B$ such that $A B=4$, then the angle made by the line $L$ with positive $X$-axis in anti-clockwise direction is

$\tan ^{-1}\left(-\frac{3}{4}\right)$

$\tan ^{-1}\left(\frac{3}{4}\right)$

$\frac{\pi}{4}$

$-\frac{\pi}{4}$

TG EAPCET 2025 (Online) 2nd May Morning Shift

MCQ (Single Correct Answer)

-0

A variable straight-line $L$ with negative slope passes through the point $(4,9)$ and cuts the positive coordinate axes in $A$ and $B$. If $O$ is the origin, then the minimum value of $O A+O B$ is

TG EAPCET 2025 (Online) 2nd May Morning Shift

MCQ (Single Correct Answer)

-0

If $4 x^2+12 x y+9 y^2+2 g x+2 f y-1=0$ represent a pair of parallel lines, then

$\frac{f}{g}+\frac{g}{f}+\frac{13}{6}=0$

$f^2+g^2=f g$

$f^2+g^2=6 f g$

$\frac{f}{g}+\frac{g}{f}=\frac{13}{6}$

TG EAPCET 2024 (Online) 11th May Morning Shift

MCQ (Single Correct Answer)

-0

$(a, b)$ is the point to which the origin has to be shifted by translation of axes so as to remove the first-degree terms from the equation $2 x^{2}-3 x y+4 y^{2}+5 y-6=0$. If the angle by which the axes are to be rotated in positive direction about the origin to remove the $x y$-term from the equation $a x^{2}+23 a b x y+b y^{2}=0$ is $\theta$, then $\tan 2 \theta=$

$\frac{\pi}{4}$

$\frac{\pi}{3}$

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