AIEEE 2010 | Circle Question 166 | 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 2009

MCQ (Single Correct Answer)

-1

Three distinct points A, B and C are given in the 2 -dimensional coordinates plane such that the ratio of the distance of any one of them from the point $$(1, 0)$$ to the distance from the point $$(-1, 0)$$ is equal to $${1 \over 3}$$. Then the circumcentre of the triangle ABC is at the point :

$$\left( {{5 \over 4},0} \right)$$

$$\left( {{5 \over 2},0} \right)$$

$$\left( {{5 \over 3},0} \right)$$

$$\left( {0,0} \right)$$

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 :

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

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

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