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1

### IIT-JEE 1994

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

The locus of a variable point whose distance from $$\left( { - 2,\,0} \right)$$ is $$2/3$$ times its distance from the line $$x = - {9 \over 2}$$ is
A
ellipse -
B
parabola
C
hyperbola
D
none of these
3

### IIT-JEE 1992

If the sum of the distances of a point from two perpendicular lines in a plane is 1, then its locus is
A
square
B
circle
C
straight line
D
two intersecting lines
4

### IIT-JEE 1990

Line $$L$$ has intercepts $$a$$ and $$b$$ on the coordinate axes. When the axes are rotated through a given angle, keeping the origin fixed, the same line $$L$$ has intercepts $$p$$ and $$q$$, then
A
$${a^2} + {b^2} = {p^2} + {q^2}$$
B
$${1 \over {{a^2}}} + {1 \over {{b^2}}} = {1 \over {{p^2}}} + {1 \over {{q^2}}}$$
C
$${a^2} + {p^2} = {b^2} + {q^2}$$
D
$${1 \over {{a^2}}} + {1 \over {{p^2}}} = {1 \over {{b^2}}} + {1 \over {{q^2}}}$$

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Class 12