1
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The locus of the mid-point of the portion of the line $x \cos \alpha+y \sin \alpha=p$ intercepted by the coordinate axes, where $p$ is a constant, is
A
$\frac{1}{x^2}+\frac{1}{y^2}=\frac{3}{p^2}$
B
$\frac{1}{x^2}+\frac{1}{y^2}=\frac{4}{p^2}$
C
$x^2+y^2=2 p^2$
D
$\frac{2}{x^2}+\frac{2}{y^2}=\frac{1}{p^2}$
2
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The origin is shifted to the point $(2,3)$ by translation of axes and then the coordinate axes are rotated about the origin through an angle $\theta$ in the counter - clockwise sense. Due to this if the equation $3 x^2+2 x y+3 y^2-18 x-22 y+50=0$ is transformed to $4 x^2+2 y^2-1=0$, then the angle $\theta$ is euqal to
A
$\frac{\pi}{4}$
B
$\frac{\pi}{3}$
C
$\frac{\pi}{6}$
D
$\frac{\pi}{2}$
3
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If the straight line passing through $P(3,4)$ makes an angle $\frac{\pi}{6}$ with the positive $X$-axis in anti-clockwise direction and meets the line $12 x+5 y+10=0$ at $Q$, then the length of the segment $P Q$ is
A
$\frac{64}{12 \sqrt{2}+1}$
B
$\frac{96}{9 \sqrt{2}-1}$
C
$\frac{112}{10 \sqrt{3}+3}$
D
$\frac{132}{12 \sqrt{3}+5}$
4
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The equation of the perpendicular bisectors of the sides $A B$ and $A C$ of $\triangle A B C$ are $x-y+5=0$ and $x+2 y=0$ respectively, If the coordinates of $A$ are $(1,-2)$, then the equal of the line $B C$ is
A
$14 x+23 y-40=0$
B
$13 x-9 y-14=0$
C
$9 x-14 y-25=0$
D
$8 x+15 y-30=0$
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