1
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$2 x^2-3 x y-2 y^2=0$ represents two lines $L_1$ and $L_2$. $2 x^2-3 x y-2 y^2-x+7 y-3=0$ represents another two lines $L_3$ and $L_4$. Let $A$ be the point of intersection of lines $L_1, L_3$ and $B$ be the point of intersection of lines $L_2$ and $L_4$. The area of the triangle formed by lines $A B$. $L_3$ and $L_4$ is
A
$3 / 10$
B
$3 / 5$
C
$45 / 2$
D
$5 / 2$
2
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The area of the triangle formed by the pair of lines $23 x^2-48 x y+3 y^2=0$ with the line $2 x+3 y+5=0$, is
A
$\frac{1}{13 \sqrt{3}}$
B
$\frac{25}{13 \sqrt{3}}$
C
$\frac{7}{13 \sqrt{5}}$
D
$\frac{9}{25 \sqrt{3}}$
3
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $\theta$ is the angle between the tangents drawn from the point $(2,3)$ to the circle $x^2+y^2-6 x+4 y+12=0$ then $\theta=$
A
$\cos ^{-1}\left(\frac{5}{13}\right)$
B
$\sin ^{-1}\left(\frac{4}{5}\right)$
C
$2 \tan ^{-1}\left(\frac{5}{12}\right)$
D
$\tan ^{-1}\left(\frac{5}{12}\right)$
4
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $2 x-3 y+3=0$ and $x+2 y+k=0$ are conjugate lines with respect to the circle $S=x^2+y^2+8 x-6 y-24=0$, then the length of the tangent drawn from the point $\left(\frac{k}{4}, \frac{k}{3}\right)$ to the circle $S=0$, is
A
7
B
1
C
12
D
24
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