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class 11th maths formulas

If the point (x,y) is equidistant from the points (a+b,b-a) and (a-b,a+b),prove that bx=ay.the vertices of a triangle ABC are A (3,2,0), B(5,3,2) and C (-9,6,-3). the bisector AD of angle A meets BC at D. find the coordinates of D.

find the ratio in which the join of A (2,1,5) b(3,4,3) is divided by the plane 2x+2y-2z =1..also find coordinates of the pt. of division ?

Find the ratio in which the sphere x

^{2}+ y^{2}+ z^{2}= 504 divides the line joining the points (12, -4, 8) and (27, -9, 18). PLZZZZZZ GIVE THE ANSWER BY TODAY ITSELF!!!!!!!!!!!!!!!!. I will give thumbs up to those who will give me the answer!!!!!!!!!!!!!!!!.Find the equation of the ellipse which passes through the point, [4,1] and having its foci at [+-3,0].

and length of the diagonal. Explain with suitable diagram.

finding the locus of a midpoint of the portion of the line xcosA+ysinA=p which is intercepted between the axes

1) In triangle ADE, BC is parallel to DE. Ar of triangle ABC = 25 sq.cm, ar of trapezium BCED = 24 sq.cm and DE = 14 cm. Calculate the length of BC. (this I found to be 10 cm). Also find the area of triangle BCD. ( I am stuck here).

2) In a trapezium ABCD, AB is parallel to DC and diagonals AC and BD intersect at point P. If AP : CP = 3 : 5, find : a) triangle APB : triangle CPB (b) triangle DPC : triangle APB (c) triangle ADP : triangle APB (d) triangle APB : triangle ADB.

^{7}in ( ax^{2}+ 1/bx)^{11}and the coefficient of x^{-7 }in (ax - 1/bx^{2})^{11 }. if these coefficients are equal then find the relation between a and bFind the coordinates of the points which trisect the line segment joining the points P (4, 2, –6) and Q (10, –16, 6).

This is an exercise question(ex 12.3,Q-5)

couldn't we do the same problem like this:

if it is a trisect then first we can find the mid point of PQ,say R

And then wouldn't the midpoint of R&P,R&Q be the points required????

huh????

find the distance of the point P(-4,3,5) from the coordinate axes.

plz answer asap

[Given ans: pq] I am getting answer as 2pq... Please answer fast

find the coorinates of the center of the circle inscribed in the triangle whose vertices are (-36,7)(20,7)(0,-8)

Find the distance of the point (3,4,5) from x-axis.

Show that the plane ax + by + cz + d = 0 divides the line joining the points(x

_{1}, y_{1}, z_{1}) and (x_{2}, y_{2}, z_{2}) in the ratio- ax

_{1}+ by_{1}+ cz_{1}+ d / ax_{2}+ by_{2}+ cz_{2}+ d .Plzzzz answer to my question!!!!!!. I will give thumbs up surely!!!!!!!!!!.The vertices of

a triangle are A(5,4,6) ,B(1,-1,3)&C(4,3,2). The internal bisector of angleA meetsBC at D. Find the coordinates of D and the length ADA is a point ( 1,3,4 ) and B is the point ( 1,-2,-1 ). A point P moves so that 3PA = 2PB find the locus of P

A(1,-1,-3),B(2,1,-2)C(-5,2,-6) are the position vectors of the vertices of a triangle ABC. The length of the bisector of its internal angle at A is?

find the equation of the locus of the point which moves such that the ratio of the distances from (2,0)and (1,3)is 5:4

Find the equation of the set of points P,the sum of whose distances from A(4,0,0)and B(-4,0,0) is 10

In a regular hexagon ABCDEF, prove that-

AB +AC + AD + AE + AF = 3AD = 6AO ; where O is the centre of the hexagon.

( AB, AC...AO- are all vectors)

(1, 0, -1), and the Three edges from this vertex are, respectively, parallel to the negativexandyaxes and positivez- axis. Find the coordinates of the other vertices of the cube.what do you mean by external and internal division?

Find the coordinates of the point which divides the line segment joining the points (–2, 3, 5) and (1, –4, 6) in the ratio (i) 2:3 internally, (ii) 2:3 externally.

what is the meaning of externally dividing a line segment?

pl answer asap

thank you

Derive an expression for the coordinates of a point that divides the line joining the points A(x1,y1,z1) and B(x2,y2,z2) internally in the ratio m:n .Hence find the coordinates of the midpoint of AB where A=(1,2,3) and B=(5,6,7).

Find the ratio in which the YZ-plane divides the line segment formed by joining the points (–2, 4, 7) and (3, –5, 8).

_{1,}y_{1,}z_{1}) and (x_{2,}y_{2,}z_{2}). Hence find the distance betweeen the point p(1,-3,4) and (-4,1,2)find the points on z axis which is equidistance from poinnt A (1,5,7) and B (5,1,-4).

the vertices of triangle ABC are A(0,0) B(2,-1) C(9,2),find cosB

the coordinate of points P,Q,R and S are (-3,5), (4,-2), (p,3p) (6,3), respectively, and the areas of triangle PQR and QRS are in ratio 2:3 .find the value of p.

Determine the point in XY plane which is equidistant from the points

A (1, –1, 0) B(2, 1, 2) and C(3, 2, –1)

Is there any trick to remember the sign conventions in each octant???????

Find the equation of the locus of a point whose distance from y axis is equal to distane from (2,1,-1) ?ANSy2-2y-4x+2z+6=0Find the distance of the point (1,2,0) from the point where the line joining A(2,-3,1) and B(3,-4,5) into the plane 2x+y+z=7?

what is the value of 3 root 3

Using section formula, prove that the points (-4,6,10) , (2,4,6) and (14,0,-2) are collinear.

Find the centroid of the triangle, the midpoint of whose sides are D(1,2,-3), E(3,0,1) and F(-1,1,4).

Show that the sum of three vectors determined by the medians of a triangle directed from the vertices is zero.

Three vertices of a parallelogram ABCD are A (3, –1, 2), B (1, 2, –4) andC (–1, 1, 2). Find the coordinates of the fourth vertex.

The centroid of an equi. triangle is (0,0) . If two vertices of the triangle lie on x+y = 2root2 then one of them will have coordinates as

Ans: (root2+root6. root2-root6)

Prove that the tetrahedron with vertices at the points

O(0, 0, 0),A(0, 1, 1),B(1, 0, 1) andC(1, 1, 0) is a regular one.find the equation of set of points P such that PA

^{2}+PB^{2}=2K2 ,where A&B are the points (3,4,5) and (-1,3-7) respectivelya circle has its centre at the origin and a radius of root 12 .state wether each of the following point is on,outside or inside the circle(1,-root 17),(3,5),(2,2root 2)

find values of A and B so that the points (a,b,3), (2,0,-1), and (1,-1,3) are collinear

1. 1:4; 3:2

2. 4:1 : 3:2

3. 4:1; 1:2

4, 4:1; 2:3

ABCD is a parallelogram and P is a point on the segment AD dividing it internally in the ratio 3:1 the line BP meets the diagonal AC in Q, Then the ratio AQ:QC is

1. 3:4

2. 4:3

3. 3:2

4. 2:3

Find the distance between(-3,4,6) and its image in XY-plane.

Find the lengths of the medians of the triangle with vertices A (0, 0, 6), B (0, 4, 0) and (6, 0, 0).