1
MHT CET 2023 10th May Morning Shift
+2
-0

If the circles $$x^2+y^2=9$$ and $$x^2+y^2+2 \alpha x+2 y+1=0$$ touch each other internally, then the value of $$\alpha^3$$ is

A
$$\frac{27}{64}$$
B
$$\frac{125}{27}$$
C
$$\frac{27}{125}$$
D
$$\frac{64}{27}$$
2
MHT CET 2023 9th May Evening Shift
+2
-0

The sides of a rectangle are given by the equations $$x=-2, x=4, y=-2$$ and $$y=5$$

Then the equation of the circle, whose centre is the point of intersection of the diagonals, lying within the rectangle and touching only two opposite sides, is

A
$$x^2+y^2+2 x+3 y+9=0$$
B
$$x^2+y^2-2 x+3 y+9=0$$
C
$$x^2+y^2+2 x-3 y-9=0$$
D
$$x^2+y^2-2 x-3 y-9=0$$
3
MHT CET 2023 9th May Morning Shift
+2
-0

Two tangents to the circle $$x^2+y^2=4$$ at the points $$\mathrm{A}$$ and $$\mathrm{B}$$ meet at the point $$\mathrm{P}(-4,0)$$. Then the area of the quadrilateral $$\mathrm{PAOB}, \mathrm{O}$$ being the origin, is

A
$$2 \sqrt{3}$$ sq. units
B
$$8 \sqrt{3}$$ sq. units
C
$$4 \sqrt{3}$$ sq. units
D
$$6 \sqrt{3}$$ sq. units
4
MHT CET 2022 11th August Evening Shift
+2
-0

If the lines $$3 x-4 y-7=0$$ and $$2 x-3 y-5=0$$ pass through diameters of a circle of area $$49 \pi$$ square units, then the equation of the circle is

A
$$x^2+y^2-2 x+2 y-47=0$$
B
$$x^2+y^2-2 x+2 y+51=0$$
C
$$x^2+y^2+2 x-2 y-51=0$$
D
$$x^2+y^2+2 x+2 y+47=0$$
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