Through a point `P(h,k,l)` a plane is drawn at right 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

A plane is passing through a point P(a, –2a, 2a), a ne 0 , at right angle to OP, where O is the origin to meet the axes in A, B and C. Find the area of the triangle ABC.

A plane a constant distance p from the origin meets the coordinate axes in A, B, C. Locus of the centroid of the triangle ABC is

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 .

Through the point ( alpha,beta, gamma) a plane is drawn perpendicular to OP where O is the origin. Let the plane meet the coordinate axes at L,M,N. Show that the area of the triangle LMN = r^5/ (2 alpha beta gamma)

A point P moves on a plane (x)/(a)+(y)/(b)+(z)/(c)=1 . A plane through P and perpendicular to OP meets the coordinate axes in A, B and C. If the planes throught A, B and C parallel to the planes x=0, y=0 and z=0 intersect in Q, then find the locus of Q.

A variable plane is at a constant distance 3p from the origin and meets the coordinates axes in A,B and C if the centroid of triangle ABC is (alpha,beta,gamma ) then show that alpha^(-2)+beta^(-2)+gamma^(-2)=p^(-2)