AIEEE 2003 | Circle Question 182 | 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 2003

MCQ (Single Correct Answer)

-1

The lines 2x - 3y = 5 and 3x - 4y = 7 are diameters of a circle having area as 154 sq. units. Then the equation of the circle is :

$${x^2}\, + \,{y^2} - \,2x\, + \,2y\,\, = \,62$$

$${x^2}\, + \,{y^2} + \,2x\, - \,2y\,\, = \,62$$

$${x^2}\, + \,{y^2} + \,2x\, - \,2y\,\, = \,47$$

$${x^2}\, + \,{y^2} - \,2x\, + \,2y\,\, = \,47$$

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 :

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

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

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

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