1
TG EAPCET 2024 (Online) 9th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
$L_1 \equiv 2 x+y-3=0$ and $L_2 \equiv a x+b y+c=0$ are two equal sides of an isosceles triangle. If $L_3 \equiv x+2 y+1=0$ is the third side of this triangle and $(5,1)$ is a point on $L_2=$ 0 , then $\frac{b^2}{|a c|}=$
A
$\frac{121}{2}$
B
$\frac{49}{52}$
C
$\frac{81}{49}$
D
$\frac{25}{4}$
2
TG EAPCET 2024 (Online) 9th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
The slope of one of the pair of lines $2 x^2+h x y+6 y^2=0$ is thrice the slope of the other line, then $h=$
A
$\pm 16$
B
$\pm 9$
C
$\pm 18$
D
$\pm 8$
3
TG EAPCET 2024 (Online) 9th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
When the origin is shifted to the point $(2, b)$ by translation of axes, the coordinates of the point $(a, 4)$ have changed to $(6,8)$. When the origin is shifted to $(a, b)$ by translation of axes, if the transformed equation of $x^2+4 x y+y^2=0$ is $X^2+2 H X Y+Y^2+2 G X+2 F Y+C=0$, then $2 H(G+F)=$
A
$C$
B
$-2 C$
C
$2 C$
D
-C
4
TG EAPCET 2024 (Online) 9th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The slope of a line $L$ passing through the point $(-2,-3)$ is not defined. If the angle between the lines $L$ and $a x-2 y+3=0(a>0)$ is $45^{\circ}$, then the angle made by the line $x+a y-4 \doteq 0$ with positive $X$-axis in the anti-clockwise direction is
A
$\pi-\tan ^{-1}\left(\frac{1}{2}\right)$
B
$\frac{\pi}{3}$
C
$\frac{2 \pi}{3}$
D
$\tan ^{-1}\left(\frac{1}{2}\right)$
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