AIEEE 2003 | Circle Question 183 | Mathematics

If the two circles $${(x - 1)^2}\, + \,{(y - 3)^2} = \,{r^2}$$ and $$\,{x^2}\, + \,{y^2} - \,8x\, + \,2y\, + \,\,8\,\, = 0$$ intersect in two distinct point, then :

$$r > 2$$

$$2 < r < 8$$

$$r < 2$$

$$r = 2.$$

AIEEE 2002

MCQ (Single Correct Answer)

-1

Out of Syllabus

The centres of a set of circles, each of radius 3, lie on the circle $${x^2}\, + \,{y^2} = 25$$. The locus of any point in the set is :

$$4\, \le \,\,{x^2}\, + \,{y^2}\, \le \,\,64$$

$${x^2}\, + \,{y^2}\, \le \,\,25$$

$${x^2}\, + \,{y^2}\, \ge \,\,25$$

$$3\, \le \,\,{x^2}\, + \,{y^2}\, \le \,\,9$$

AIEEE 2002

MCQ (Single Correct Answer)

-1

If the chord y = mx + 1 of the circle $${x^2}\, + \,{y^2} = 1$$ subtends an angle of measure $${45^ \circ }$$ at the major segment of the circle then value of m is :

$$2\, \pm \,\sqrt 2 \,\,$$

$$ - \,2\, \pm \,\sqrt 2 \,$$

$$- 1\, \pm \,\sqrt 2 \,\,$$

none of these

AIEEE 2002

MCQ (Single Correct Answer)

-1

The equation of a circle with origin as a center and passing through an equilateral triangle whose median is of length $$3$$$$a$$ is :

$${x^2}\, + \,{y^2} = 9{a^2}$$

$${x^2}\, + \,{y^2} = 16{a^2}$$

$${x^2}\, + \,{y^2} = 4{a^2}$$

$${x^2}\, + \,{y^2} = {a^2}$$