1
AIEEE 2010
+4
-1
The circle $${x^2} + {y^2} = 4x + 8y + 5$$ intersects the line $$3x - 4y - m$$ at two distinct points if
A
$$- 35 < m < 15$$
B
$$15 < m < 65$$
C
$$35 < m < 85$$
D
$$- 85 < m < -35$$
2
AIEEE 2009
+4
-1
If $$P$$ and $$Q$$ are the points of intersection of the circles
$${x^2} + {y^2} + 3x + 7y + 2p - 5 = 0$$ and $${x^2} + {y^2} + 2x + 2y - {p^2} = 0$$ then there is a circle passing through $$P,Q$$ and $$(1, 1)$$ for:
A
all except one value of $$p$$
B
all except two values of $$p$$
C
exactly one value of $$p$$
D
all values of $$p$$
3
AIEEE 2008
+4
-1
The point diametrically opposite to the point $$P(1, 0)$$ on the circle $${x^2} + {y^2} + 2x + 4y - 3 = 0$$ is
A
$$(3, -4)$$
B
$$(-3, 4)$$
C
$$(-3, -4)$$
D
$$(3, 4)$$
4
AIEEE 2008
+4
-1
The differential equation of the family of circles with fixed radius $$5$$ units and centre on the line $$y = 2$$ is
A
$$\left( {x - 2} \right){y^2} = 25 - {\left( {y - 2} \right)^2}$$
B
$$\left( {y - 2} \right){y^2} = 25 - {\left( {y - 2} \right)^2}$$
C
$${\left( {y - 2} \right)^2}{y^2} = 25 - {\left( {y - 2} \right)^2}$$
D
$${\left( {x - 2} \right)^2}{y^2} = 25 - {\left( {y - 2} \right)^2}$$
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