1
IIT-JEE 1998
MCQ (Single Correct Answer)
+2
-0.5
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
$$12$$
2
IIT-JEE 1998
MCQ (Single Correct Answer)
+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.
3
IIT-JEE 1998
Subjective
+8
-0
$$C_1$$ and $$C_2$$ are two concentric circles, the radius of $$C_2$$ being twice that of $$C_1$$. From a point P on $$C_2$$, tangents PA and PB are drawn to $$C_1$$. Prove that the centroid of the triangle PAB lies on $$C_1$$.
4
IIT-JEE 1998
MCQ (More than One Correct Answer)
+2
-0.5
If the circle $${x^2}\, + \,{y^2} = \,{a^2}$$ intersects the hyperbola $$xy = {c^2}$$ in four points $$P\,({x_1},\,{y_1}),\,Q\,\,({x_2},\,{y_2}),\,\,R\,({x_3},\,{y_3}),\,S\,({x_4},\,{y_4}),$$ then
A
$${x_1}\, + \,{x_2} + \,{x_3}\, + \,{x_4}\, = 0$$
B
$${y_1}\, + \,{y_2} + \,{y_3}\, + \,{y_4}\, = 0$$
C
$${x_1}\,{x_2}\,{x_3}\,{x_4}\, = {c^4}$$
D
$${y_1}\,{y_2}\,{y_3}\,{y_4}\, = {c^4}$$
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