1
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
Locus of centroid of the triangle whose vertices are $$\left( {a\cos t,a\sin t} \right),\left( {b\sin t, - b\cos t} \right)$$ and $$\left( {1,0} \right),$$ where $$t$$ is a parameter, is :
A
$${\left( {3x + 1} \right)^2} + {\left( {3y} \right)^2} = {a^2} - {b^2}$$
B
$${\left( {3x - 1} \right)^2} + {\left( {3y} \right)^2} = {a^2} - {b^2}$$
C
$${\left( {3x - 1} \right)^2} + {\left( {3y} \right)^2} = {a^2} + {b^2}$$
D
$${\left( {3x + 1} \right)^2} + {\left( {3y} \right)^2} = {a^2} + {b^2}$$
2
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
If the equation of the locus of a point equidistant from the point $$\left( {{a_{1,}}{b_1}} \right)$$ and $$\left( {{a_{2,}}{b_2}} \right)$$ is
$$\left( {{a_1} - {a_2}} \right)x + \left( {{b_1} - {b_2}} \right)y + c = 0$$ , then the value of $$'c'$$ is :
A
$$\sqrt {{a_1}^2 + {b_1}^2 - {a_2}^2 - {b_2}^2} $$
B
$${1 \over 2}\left( {{a_2}^2 + {b_2}^2 - {a_1}^2 - {b_1}^2} \right)$$
C
$${{a_1}^2 - {a_2}^2 + {b_1}^2 - {b_2}^2}$$
D
$${1 \over 2}\left( {{a_1}^2 + {a_2}^2 + {b_1}^2 + {b_2}^2} \right)$$.
3
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
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 :
A
$$r > 2$$
B
$$2 < r < 8$$
C
$$r < 2$$
D
$$r = 2.$$
4
AIEEE 2003
MCQ (Single Correct Answer)
+4
-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 :
A
$${x^2}\, + \,{y^2} - \,2x\, + \,2y\,\, = \,62$$
B
$${x^2}\, + \,{y^2} + \,2x\, - \,2y\,\, = \,62$$
C
$${x^2}\, + \,{y^2} + \,2x\, - \,2y\,\, = \,47$$
D
$${x^2}\, + \,{y^2} - \,2x\, + \,2y\,\, = \,47$$
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