`O A` and `O B` are fixed straight lines, `P` is any point and `P M` and `P N` are the perpendiculars from `P` on `O Aa n dO B ,` respectively. Find the locus of `P` if the quadrilateral `O M P N` is of constant area.

O P Q R is a square and M ,N are the middle points of the sides P Qa n dQ R , respectively. Then the ratio of the area of the square to that of triangle O M N is 4:1 (b) 2:1 (c) 8:3 (d) 7:3

In fig. 28.7 if the coordinates of point P a r e (a , b , c) then Write the coordinates of points A, B, C, D, E and F. Write the coordinates of the feet of the perpendiculars from the point P to the coordinate axes. Write the coordinates of the feet of the perpendicular from the point P on the coordinate planes X Y , Y Z a n d Z Xdot Find the perpendicular distances of point P from X Y , Y Z a n d Z X- planes. Find the perpendicular distances of the point P fro the coordinate axes. Find the coordinates of the reflection of P are (a , b , c) . Therefore O A=a , O B=b n d O C=cdot

The line x+y=p meets the x- and y-axes at Aa n dB , respectively. A triangle A P Q is inscribed in triangle O A B ,O being the origin, with right angle at QdotP and Q lie, respectively, on O Ba n dA B . If the area of triangle A P Q is 3/8t h of the are of triangle O A B , the (A Q)/(B Q) is equal to (a)2 (b) 2/3 (c) 1/3 (d) 3

Two tangents P Aa n dP B are drawn from an external point P to a circle with centre Odot Prove that A O B P is a cyclic quadrilateral.

M is the son of N. O is the father of N. P is the father of M. How is N related to P?

O P Q R is a square and M ,N are the midpoints of the sides P Q and Q R , respectively. If the ratio of the area of the square to that of triangle O M N is lambda:6, then lambda/4 is equal to 2 (b) 4 (c) 2 (d) 16

Of all the line segments that can be drawn to a given line, from a point, not lying on it, the perpendicular line segment is the shortest. GIVEN : A straight line l and a point P not lying on ldot P M_|_l and N is any point on 1 other than Mdot TO PROVE : P M

A straight line is drawn from a fixed point O meeting a fixed straight line in P . A point Q is taken on the line OP such that OP.OQ is constant. Show that the locus of Q is a circle.