1
AP EAPCET 2022 - 4th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

If the lines represented by $$a x^2+2 h x y+b y^2+2 g x+2 f y+c=0$$ intersect on the $$X$$-axis, which of the following is in general incorrect?

A
$$a b c=2 f g h$$
B
$$g^2=a c$$
C
$$a f^2=c h^2$$
D
$$a f^2+c h^2=2 f g h$$
2
AP EAPCET 2022 - 4th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

For $$\alpha \in\left[0, \frac{\pi}{2}\right]$$, the angle between the lines represented by $$[x \cos \theta-y] [(\cos \theta+\tan \alpha) x-(1-\cos \theta \tan \alpha) y]=0$$ is

A
$$\alpha$$
B
$$\theta$$
C
$$\theta+\alpha$$
D
$$\theta-\alpha$$
3
AP EAPCET 2022 - 4th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

The locus of centers of the circles, possessing the same area and having $$3 x-4 y+4=0$$ and $$6 x-8 y-7=0$$ as their common tangent, is

A
$$12 x-16 y-15=0$$
B
$$3 x-4 y+\frac{11}{2}=0$$
C
$$12 x-16 y+15=0$$
D
$$3 x-4 y-\frac{11}{2}=0$$
4
AP EAPCET 2022 - 4th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

For any two non-zero real numbers $$a$$ and $$b$$ if this line $$\frac{x}{a}+\frac{y}{b}=1$$ is a tangent to the circle $$x^2+y^2=1$$, then which of the following is true?

A
$$\left(\frac{1}{a}, \frac{1}{b}\right)$$ lies inside the circle
B
$$(a, b)$$ lies inside the circle
C
$$\left(\frac{1}{a}, \frac{1}{b}\right)$$ lies on the circle
D
$$(a, b)$$ lies on the circle.
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