1
AP EAPCET 2022 - 4th July Evening Shift
+1
-0

If the pair of straight lines $$9 x^2+a x y+4 y^2+6 x+b y-3=0$$ represents two parallel lines, then

A
$$a=6, b=2$$
B
$$a=12, b=4$$
C
$$a=3, b=1$$
D
$$a=-12, b=4$$
2
AP EAPCET 2022 - 4th July Evening Shift
+1
-0

A line passing through $$P(2,3)$$ and making an angle of $$30^{\circ}$$ with the positive direction of $$X$$-axis meets $$x^2-2 x y-y^2=0$$ at $$A$$ and $$B$$. Then the value of $$P A: P B$$ is

A
$$17 \sqrt{3}+1$$
B
$$17(\sqrt{3}+1)$$
C
$$17(\sqrt{3}-1)$$
D
$$17 \sqrt{3}-1$$
3
AP EAPCET 2022 - 4th July Morning Shift
+1
-0

The least distance from origin to a point on the line $$y=x+3$$ which lies at a distance of 2 units from $$(0,3)$$ is

A
$$13+6 \sqrt{2}$$
B
$$10+6 \sqrt{2}$$
C
$$10-6 \sqrt{2}$$
D
$$13-6 \sqrt{2}$$
4
AP EAPCET 2022 - 4th July Morning Shift
+1
-0

Starting from the point $$A(-3,4)$$, a moving object touches $$2 x+y-7=0$$ at $$B$$ and reaches the point $$C(0,1)$$. If the object travels along the shortest path, the distance between $$A$$ and $$B$$ is

A
$$\frac{68}{\sqrt{170}}$$
B
$$\frac{9}{\sqrt{5}}$$
C
$$3 \sqrt{2}$$
D
$$\frac{6}{\sqrt{5}}$$
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