Through a point `P(h,k,l)` a plane is drawn at righat angle to `OP` to meet the coordinate axes in `A,B` and `C`. If `OP =p` show that the area of `/_\ABC` is `p^5/(2hkl)`

Through the point P(h, k, l) a plane is drawn at right angles to OP to meet co-ordinate axes at A, B and C. If OP=p, A_xy is area of projetion of triangle(ABC) on xy-plane. A_zy is area of projection of triangle(ABC) on yz-plane, then

Find the eqution of the curve passing through the point (1,1), if the tangent drawn at any point P(x,y) on the curve meets the coordinate axes at A and B such that P is the mid point of AB.

A line is drawn passing through point P(1,2) to cut positive coordinate axes at A and B . Find minimum area of DeltaPAB .

A variable plane is at a constant distance p from the origin and meets the coordinate axes in A , B , C . Show that the locus of the centroid of the tetrahedron O A B C is x^(-2)+y^(-2)+z^(-2)=16p^(-2)

A variable plane which remains at a constant distance 3p from the origin cuts the coordinate axes at A, B, C. Show that the locus of the centroid of triangle ABC is x^(-2) + y^(-2) + z^(-2) = p^(-2) .

From a point P, two tangents PA and PB are drawn to a circle with centre O and radius r. If OP=2r, show that triangleAPB is equilateral.

Let P(alpha,beta) be a point in the first quadrant. Circles are drawn through P touching the coordinate axes. Radius of one of the circles is

A straight line is drawn through the point P(2,3)and is inclined at an angle of 30^@ with the x axis. Then the coordinates of two points on it at a distance 4 from P on either side of P will be..

Find the foot of perpendicular drawn from a point P(2, 3, 5) on the coordinate planes.

Find the foot of perpendicular drawn from a point P(2, 4, -5) on the coordinate planes.