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1

IIT-JEE 1999

MCQ (Single Correct Answer)
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
2

IIT-JEE 1999

MCQ (Single Correct Answer)
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
$$ - \left( {{{{a^2} + {b^2}} \over b}} \right)$$
3

IIT-JEE 1998

MCQ (Single Correct Answer)
If $$P=(x, y)$$, $${F_1} = \left( {3,0} \right),\,{F_2} = \left( { - 3,0} \right)$$ and $$16{x^2} + 25{y^2} = 400,$$ then $$P{F_1} + P{F_2}$$ equals
A
$$8$$
B
$$6$$
C
$$10$$
D
$$12$$
4

IIT-JEE 1998

MCQ (Single Correct Answer)
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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