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

If the normal to the rectangular hyperbola $$x^2-y^2=1$$ at the point $$P(\pi / 4)$$ meets the curve again at $$Q(\theta)$$, then $$\sec ^2 \theta+\tan \theta=$$

A
43
B
57
C
3
D
1
2
AP EAPCET 2022 - 4th July Evening Shift
+1
-0

If the vertices and foci of a hyperbola are respectively $$( \pm 3,0)$$ and $$( \pm 4,0)$$, then the parametric equations of that hyperbola are

A
$$x=3 \sec \theta, y=7 \tan \theta$$
B
$$x=\sqrt{3} \sec \theta, y=\sqrt{7} \tan \theta$$
C
$$x=\sqrt{3} \sec \theta, y=7 \tan \theta$$
D
$$x=3 \sec \theta, y=\sqrt{7} \tan \theta$$
3
AP EAPCET 2022 - 4th July Morning Shift
+1
-0

The value of $$\frac{1+\tan \mathrm{h} x}{1-\tan \mathrm{h} x}$$ is

A
$$e^x$$
B
$$e^{-2 x}$$
C
$$e^{2 x}$$
D
$$e^{-x}$$
4
AP EAPCET 2022 - 4th July Morning Shift
+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.
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