1
IIT-JEE 1994
MCQ (Single Correct Answer)
+2
-0.5
The equations to a pair of opposites sides of parallelogram are $${x^2} - 5x + 6 = 0$$ and $${y^2} - 6y + 5 = 0,$$ the equations to its diagonals are
A
$$x + 4y = 13,\,y = 4x - 7$$
B
$$4x + y = 13,\,4y = x - 7$$
C
$$4x + y = 13,\,y = 4x - 7$$
D
$$y - 4x = 13,\,y + 4x = 7$$
2
IIT-JEE 1994
MCQ (Single Correct Answer)
+1
-0.25
The circles $${x^2} + {y^2} - 10x + 16 = 0$$ and $${x^2} + {y^2} = {r^2}$$ intersect each other in two distinct points if
A
r < 2
B
r > 8
C
2 < r < 8
D
$$2 \le r \le 8$$
3
IIT-JEE 1994
Fill in the Blanks
+2
-0
The point of intersection of the tangents at the ends of the latus rectum of the parabola $${y^2} = 4x$$ is ...... .
4
IIT-JEE 1994
MCQ (Single Correct Answer)
+2
-0.5
The equation $$2{x^2} + 3{y^2} - 8x - 18y + 35 = k$$ represents
A
no locus if $$k > 0$$
B
an ellipse if $$k < 0$$
C
a point if $$k = 0$$
D
a hyperbola if $$k > 0$$
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