AIEEE 2003 (Maths) Mock Test

Locus of centroid of the triangle whose vertices are $(a\cos t,a\sin t)$, $(b\sin t,-b\cos t)$ and $(1,0)$, where $t$ is a parameter, is:

If the pair of straight lines $x^2-2pxy-y^2=0$ and $x^2-2qxy-y^2=0$ be such that each pair bisects the angle between the other pair, then:

A square of side $a$ lies above the $x$ -axis and has one vertex at the origin. The side passing through the origin makes an angle $\alpha$ ($0<\alpha <\pi /4$) with the positive direction of $x$ -axis. The equation of its diagonal not passing through the origin is:

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 points, then:

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: