If a circle of constant radius `3k` passes through the origin `O` and meets the coordinate axes at `Aa n dB` , then the locus of the centroud of triangle `O A B` is (a)`x^2+y^2=(2k)^2` (b)`x^2+y^2=(3k)^2` (c)`x^2+y^2=(4k)^2` (d) `x^2+y^2=(6k)^2`

A sphere of constant radius k , passes through the origin and meets the axes at A ,Ba n d Cdot Prove that the centroid of triangle A B C lies on the sphere 9(x^2+y^2+z^2)=4k^2dot

A sphere of constant radius 2k passes through the origin and meets the axes in A ,B ,a n dCdot The locus of a centroid of the tetrahedron O A B C is a. x^2+y^2+z^2=4k^2 b. x^2+y^2+z^2=k^2 c. 2(k^2+y^2+z)^2=k^2 d. none of these

A circle of constant radius a passes through the origin O and cuts the axes of coordinates at points P and Q . Then the equation of the locus of the foot of perpendicular from O to P Q is (A) (x^2+y^2)(1/(x^2)+1/(y^2))=4a^2 (B) (x^2+y^2)^2(1/(x^2)+1/(y^2))=a^2 (C) (x^2+y^2)^2(1/(x^2)+1/(y^2))=4a^2 (D) (x^2+y^2)(1/(x^2)+1/(y^2))=a^2

The tangent at any point P on the circle x^2+y^2=4 meets the coordinate axes at Aa n dB . Then find the locus of the midpoint of A Bdot

If a circle passes through the points where the lines 3kx- 2y-1 = 0 and 4x-3y + 2 = 0 meet the coordinate axes then k=

If a circle passes through the point (a, b) and cuts the circle x^2 +y^2=k^2 orthogonally, then the equation of the locus of its center is

If points Aa n dB are (1, 0) and (0, 1), respectively, and point C is on the circle x^2+y^2=1 , then the locus of the orthocentre of triangle A B C is (a) x^2+y^2=4 (b) x^2+y^2-x-y=0 (c) x^2+y^2-2x-2y+1=0 (d) x^2+y^2+2x-2y+1=0

The locus of the center of the circle touching the line 2x-y=1 at (1,1) is (a) x+3y=2 (b) x+2y=3 (c) x+y=2 (d) none of these

If a circle of radius r is touching the lines x^2-4x y+y^2=0 in the first quadrant at points Aa n dB , then the area of triangle O A B(O being the origin) is (a) 3sqrt(3)(r^2)/4 (b) (sqrt(3)r^2)/4 (c) (3r^2)/4 (d) r^2

Let S be the circle in the x y -plane defined by the equation x^2+y^2=4. (For Ques. No 15 and 16) Let P be a point on the circle S with both coordinates being positive. Let the tangent to S at P intersect the coordinate axes at the points M and N . Then, the mid-point of the line segment M N must lie on the curve (a) (x+y)^2=3x y (b) x^(2//3)+y^(2//3)=2^(4//3) (c) x^2+y^2=2x y (d) x^2+y^2=x^2y^2