Internal Division

Q.

Point R(h, k) divides a line segment between the axis in the ratio 1: 2. Find equation of the line.

Q.

The line, which is parallel to $x-$axis and crosses the curve $y=\sqrt{x}$ at an angle $45°$, is

1. $y=\frac{1}{4}$

2. $y=\frac{1}{2}$

3. $y=1$

4. $y=4$

Q.

Find the equation of the line so that the line segment intercepted between the axes is divided by the point P(-5, 4) in the ratio 1: 2.

Q. Find the coordinates of the point which divides the join of the points P(5, 4, 2) and Q(-1, -2, 4) in the ratio 2:3.

Q.

Find the coordinates of the points which divide the line segment joining A(-2, 2) and B(2, 8) into four equal parts.

1. , (0, 5) ,

2. (-1, 7), (0, 5) , (1, 13)

3. , (0, 5) ,

4. , (0, 5) ,

Q. Find the ratio in which the join of the points P(2, -1, 3) and Q(4, 3, 1) is divided by the point $(\frac{20}{7},\frac{5}{7},\frac{15}{7})$.

Q.

Find the equation of the line which passes through the point (-4, 3) and the portion of the line intercepted between the axes is divided internally in the ratio 5:3 by this point.

Q.

A(0, 6), B(8, 12), C(8, 0) are the Co-ordinate of vertices of triangle ABC. Then......
1. Co-ordinate of centroid P.(20, 6)
2. Co-ordinate of In centre q.(0, 16)
3. Co-ordinate of Ex centre r.($\frac{16}{3}$, 6)
s.(0, -4)
t.(5, 6)

1. 1-r 2 - t 3-p

2. 1-r 2 - t 3-q

3. 1-r 2 - t 3-s

4. 1-r 2 - q 3-t

Q. The midpoint of the points on x + y = 4, which are 4 units from 4x + 3y - 10 = 0 is the point of intersection of the two lines given.

1. True

2. False

Q. $P$ and $Q$ are two points lying on the line joining the points $A(12,8)$ and $B(-2,6)$ such that $AP=PQ=QB.$ Then the midpoint of $PQ$ is

1. $(7,1)$
2. $(9,3)$
3. $(6,4)$
4. $(5,7)$

Q. A straight line through the origin O meets the parallel lines 4x+2y = 9 and 2x+y+ 6 = 0 at points P and Q respectively. Then the point O divides the segment PQ in ratio

1. 4:3
2. 1:2
3. 2:1
4. 3:4

Q. The coordinates of the foot of the perpendicular drawn form the origin to the plane $2x+3y+4z-12=0$ is

1. $(\frac{24}{29},\frac{48}{29},\frac{36}{29})$
2. $(\frac{36}{29},\frac{24}{29},\frac{48}{29})$
3. $(\frac{24}{29},\frac{36}{29},\frac{48}{29})$
4. None of these

Q.

If the origin is the centroid of the triangle with vertices P(2a, 2, 6), Q(-4, 3b, -10) and R(8, 14, 2c), find the values of a, b and c. Also, determine the value of $a^2+b^2-c^2$.

Q.

If $(-g,-f)$ is the coordinate of center circle and it follows the relation $2g+2f+5=0$, then the locus of its Centre of the circle is $2x+2y+5=0$

1. True

2. False

Q. A rod of length $l$ moves such that its ends $A$ and $B$ always lie on the lines $3x-y+5=0$ and $y+5=0$ respectively. The locus of the point $P,$ which divides $AB$ internally in the ratio $2:1,$ is $l^2=\frac{1}{k}(ax-by-5{)}^2+9(y+5{)}^2.$ Then

1. $k=4,a+b=6$
2. $k=3,a+b=5$
3. $k=4,a+b=0$
4. $k=3,a+b=4$

Q. The point A divides the join of P(-5, 1) and Q(3, 5) in the ratio k:1. Find the two values of k for which the area of $\Delta ABC$ where B is (1, 5) and C is (7, -2) is equal to 2 units.

1. undefined
2. undefined
3. undefined
4. undefined