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

The eccentric angle of a point on the ellipse $$x^2+3 y^2=6$$ lying at a distance of 2 units from its centre is

A
$$\frac{\pi}{6}$$
B
$$\frac{\pi}{4}$$
C
$$\frac{\pi}{3}$$
D
$$\frac{\pi}{2}$$
2
AP EAPCET 2022 - 4th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

Let origin be the centre, $$( \pm 3,0)$$ be the foci and $$\frac{3}{2}$$ be the eccentricity of a hyperbola. Then, the line $$2 x-y-1=0$$

A
intersects the hyperbola at two points.
B
does not intersect the hyperbola.
C
touches the hyperbola.
D
passes through the vertex of the hyperbola.
3
AP EAPCET 2022 - 4th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

The locus of a variable point whose chord of contact w.r.t. the hyperbola $$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$$ subtends a right angle at the origin is

A
$$\frac{x^2}{4 a^2}-\frac{y^2}{4 b^2}=1$$
B
$$\left(\frac{x^2}{a^2}-\frac{y^2}{b^2}\right)=\frac{x^2}{a^4}+\frac{y^2}{b^4}$$
C
$$\frac{x}{a}-\frac{y}{b}=\frac{1}{a^2}+\frac{1}{b^2}$$
D
$$\frac{x^2}{a^4}+\frac{y^2}{b^4}=\frac{1}{a^2}-\frac{1}{b^2}$$
4
AP EAPCET 2022 - 4th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

If the point $$(a, 8,-2)$$ divides the line segment joining the points $$(1,4,6)$$ and $$(5,2,10)$$ in the ratio $$m: n$$, then $$\frac{2 m}{n}-\frac{a}{3}=$$

A
$$-$$7
B
1
C
$$-$$2
D
3
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