Home
Class 12
MATHS
Given four points P1,P2,P3a n dP4 on the...

Given four points `P_1,P_2,P_3a n dP_4` on the coordinate plane with origin `O` which satisfy the condition `( vec (O P))_(n-1)+( vec(O P))_(n+1)=3/2 vec (O P)_(n)` (i) If P1 and P2 lie on the curve xy=1 , then prove that P3 does not lie on the curve (ii) If P1,P2,P3 lie on a circle `x^2+y^2=1`, then prove that P4 also lies on this circle.

Promotional Banner

Similar Questions

Explore conceptually related problems

Given four points P_1,P_2,P_3a n dP_4 on the coordinate plane with origin O which satisfy the condition ( vec (O P))_(n-1)+( vec(O P))_(n+1)=3/2 vec (O P)_(n) . If P1 and P2 lie on the curve xy=1 , then prove that P3 does not lie on the curve

Given four points P_1,P_2,P_3a n dP_4 on the coordinate plane with origin O which satisfy the condition ( vec (O P))_(n-1)+( vec(O P))_(n+1)=3/2 vec (O P)_(n) . If P1 and P2 lie on the curve xy=1 , then prove that P3 does not lie on the curve

IF P_1, P_2, P_3, P_4 are points in a plane or space and O is the origin of vectors, show that P_4 coincides with Oiff( vec O P)_1+ vec P_1P_2+ vec P_2P_3+ vec P_3P_4= vec 0.

IF P_(1),P_(2),P_(3),P_(4) are points in a plane or space and O is the origin of vectors,show that P_(4) coincides with Oiff vec OP_(1)+vec P_(1)P_(2)+vec P_(2)P_(3)+vec P_(3)P_(4)=vec 0

If p_1 and p_2 be the lengths of perpendiculars from the origin on the tangent and normal to the curve x^(2/3)+y^(2/3)= a^(2/3) respectively, then 4p_1^2 +p_2^2 =

O is the origin and A is a fixed point on the circle of radius 'a' with centre O.The vector vec O A is denoted by vec a . A variable point P lie on the tangent at A and vec OP=vec r. Show that vec a vec r=a^2. Hence if P(x, y) and A(x_1, y_1), deduce the equation of tangent at A to this circle.

O is the origin and A is a fixed point on the circle of radius 'a' with centre O.The vector vec O A is denoted by vec a . A variable point P lie on the tangent at A and vec OP-vec r. Show that vec a vec r=a^2. Hence if P(x, y) and A(x_1, y_1), deduce the equation of tangent at A to this circle.