AIEEE 2006 | Circle Question 148 | Mathematics

Let $$C$$ be the circle with centre $$(0, 0)$$ and radius $$3$$ units. The equation of the locus of the mid points of the chords of the circle $$C$$ that subtend an angle of $${{2\pi } \over 3}$$ at its center is :

$${x^2} + {y^2} = {3 \over 2}$$

$${x^2} + {y^2} = 1$$

$${x^2} + {y^2} = {{27} \over 4}$$

$${x^2} + {y^2} = {{9} \over 4}$$

AIEEE 2005

MCQ (Single Correct Answer)

-1

Out of Syllabus

A circle touches the x-axis and also touches the circle with centre at (0, 3) and radius 2. The locus of the centre of the circle is :

an ellipse

a circle

a hyperbola

a parabola

AIEEE 2005

MCQ (Single Correct Answer)

-1

If a circle passes through the point (a, b) and cuts the circle $${x^2}\, + \,{y^2} = {p^2}$$ orthogonally, then the equation of the locus of its centre is :

$${x^2}\, + \,{y^2} - \,3ax\, - \,4\,by\,\, + \,({a^2}\, + \,{b^2} - {p^2}) = 0$$

$$2ax\, + \,\,2\,by\,\, - \,({a^2}\, - \,{b^2} + {p^2}) = 0$$

$${x^2}\, + \,{y^2} - \,2ax\, - \,\,3\,by\,\, + \,({a^2}\, - \,{b^2} - {p^2}) = 0$$

$$2ax\, + \,\,2\,by\,\, - \,({a^2}\, + \,{b^2} + {p^2}) = 0$$

AIEEE 2005

MCQ (Single Correct Answer)

-1

If the circles $${x^2}\, + \,{y^2} + \,2ax\, + \,cy\, + a\,\, = 0$$ and $${x^2}\, + \,{y^2} - \,3ax\, + \,dy\, - 1\,\, = 0$$ intersect in two ditinct points P and Q then the line 5x + by - a = 0 passes through P and Q for :

exactly one value of a

no value of a

infinitely many values of a

exactly two values of a

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