AIEEE 2009 | Circle Question 138 | Mathematics

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 :

all except one value of $$p$$

all except two values of $$p$$

exactly one value of $$p$$

all values of $$p$$

AIEEE 2008

MCQ (Single Correct Answer)

-1

The point diametrically opposite to the point $$P(1, 0)$$ on the circle $${x^2} + {y^2} + 2x + 4y - 3 = 0$$ is :

$$(3, -4)$$

$$(-3, 4)$$

$$(-3, -4)$$

$$(3, 4)$$

AIEEE 2008

MCQ (Single Correct Answer)

-1

Out of Syllabus

The differential equation of the family of circles with fixed radius $$5$$ units and centre on the line $$y = 2$$ is :

$$\left( {x - 2} \right){y^2} = 25 - {\left( {y - 2} \right)^2}$$

$$\left( {y - 2} \right){y^2} = 25 - {\left( {y - 2} \right)^2}$$

$${\left( {y - 2} \right)^2}{y^2} = 25 - {\left( {y - 2} \right)^2}$$

$${\left( {x - 2} \right)^2}{y^2} = 25 - {\left( {y - 2} \right)^2}$$

AIEEE 2007

MCQ (Single Correct Answer)

-1

Out of Syllabus

Consider a family of circles which are passing through the point $$(-1, 1)$$ and are tangent to $$x$$-axis. If $$(h, k)$$ are the coordinate of the centre of the circles, then the set of values of $$k$$ is given by the interval :

$$ - {1 \over 2} \le k \le {1 \over 2}$$

$$k \le {1 \over 2}$$

$$0 \le k \le {1 \over 2}$$

$$k \ge {1 \over 2}$$

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