1
IIT-JEE 1999
+2
-0.5
Let $$P$$ $$\left( {a\,\sec \,\theta ,\,\,b\,\tan \theta } \right)$$ and $$Q$$ $$\left( {a\,\sec \,\,\phi ,\,\,b\,\tan \,\phi } \right)$$, where $$\theta + \phi = \pi /2,$$, be two points on the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$.

If $$(h, k)$$ is the point of intersection of the normals at $$P$$ and $$Q$$, then $$k$$ is equal to

A
$${{{a^2} + {b^2}} \over a}$$
B
$$- \left( {{{{a^2} + {b^2}} \over a}} \right)$$
C
$${{{a^2} + {b^2}} \over b}$$
D
$$- \left( {{{{a^2} + {b^2}} \over b}} \right)$$
2
IIT-JEE 1999
+2
-0.5
The curve described parametrically by $$x = {t^2} + t + 1,$$ $$y = {t^2} - t + 1$$ represents
A
a pair of straight lines
B
an ellipse
C
a parabola
D
a hyperbola
3
IIT-JEE 1999
+2
-0.5
If $$x$$ $$=$$ $$9$$ is the chord of contact of the hyperbola $${x^2} - {y^2} = 9,$$ then the equation of the vcorresponding pair of tangents is
A
$$9{x^2} - 8{y^2} + 18x - 9 = 0$$
B
$$9{x^2} - 8{y^2} - 18x + 9 = 0$$
C
$$9{x^2} - 8{y^2} - 18x - 9 = 0$$
D
$$9{x^2} - 8{y^2} + 18x + 9 = 0$$
4
IIT-JEE 1998
+2
-0.5
The number of values of $$c$$ such that the straight line $$y=4x + c$$ touches the curve $$\left( {{x^2}/4} \right) + {y^2} = 1$$ is
A
$$0$$
B
$$1$$
C
$$2$$
D
infinite.
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