1
AP EAPCET 2024 - 20th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If power of a point $(4,2)$ with respect to the circle $x^2+y^2-2 \alpha x+6 y+\alpha^2-16=0$ is 9 , then the sum of the lengths of all possible intercepts made by such circles on the coordinate axes is
A
$16+4 \sqrt{6}$
B
$16+4 \sqrt{6}-6 \sqrt{2}$
C
$16+4 \sqrt{6}+6 \sqrt{2}$
D
$16+6 \sqrt{2}$
2
AP EAPCET 2024 - 20th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
Let $\alpha$ be an integer multiple of 8 . If $S$ is the set of all possible values of $\alpha$ such that the line $6 x+8 y+\alpha=0$ intersects the circle $x^2+y^2-4 x-6 y+9=0$ at two distinct points, then the number of elements in $S$ is
A
4
B
6
C
2
D
1
3
AP EAPCET 2024 - 20th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If the circle $x^2+y^2-8 x-8 y+28=0$ and $x^2+y^2-8 x-6 y+25-\alpha^2=0$ have only one common tangent, then $\alpha=$
A
$\alpha=4$
B
$\alpha=2$
C
$\alpha=1$
D
$\alpha=5$
4
AP EAPCET 2024 - 20th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If the equation of the circle passing through the points of intersection of the circles $x^2-2 x+y^2-4 y-4=0$, $x^2+2 x+y^2+4 y-4=0$ and the point $(3,3)$ is given by $x^2+y^2+\alpha x+\beta y+\gamma=0$, then $3(\alpha+\beta+\gamma)=$
A
32
B
-32
C
-26
D
26
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