Distance Formula

Q.

The equation of the locus of a point whose distance from (a, 0) is equal to its distance from y-axis, is

1. 

2. 

3. 

4. 

Q.

The distance between the points P(1, –3, 4) and Q (– 4, 1, 2) is:

1. √5 units

2. 5 units

3. 2√13 units

4. 3√5units

Q.

The equation to the locus of a point which moves so that its distance from $x$-axis is always one half its distance from the origin, is

1. $x^2+3y^2=0$

2. $x^2-3y^2=0$

3. $3x^2+y^2=0$

4. $3x^2-y^2=0$

Q.

Locus of the points which are at equal distance from $3x+4y-11=0$ and $12x+5y+2=0$ and which is near the origin is

1. $21x–77y+153=0$

2. $99x+77y–133=0$

3. $7x–11y=19$

4. None of these

Q. 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 equal to 10.

Q.

If vertices of a quadrilateral are A (0, 0), B(3, 4), C(7, 7) and D(4, 3) then quadrilateral ABCD is

1. Parallelogram

2. Rectangle

3. Rhombus

4. Square

Q.

The points (3a, 0), (0, 3b) and (a, 2b) are

1. Vertices of an equilateral triangle

2. Vertices of an isosceles triangle

3. Vertices of a right angled isosceles triangle

4. Collinear

Q.

A point moves in such a way that the sum of square of its distance from the points A(2, 0) and B(-2, 0) is always

equal to the square of the distance between A and B. The locus of the point is

1. 

2. 

3. 

4. 

Q.

The coordinates of a point which is equidistant from the points $(0,0,0),(a,0,0),(0,b,0)and(0,0,c)$ are given by _____

1. 

2. 

3. 

4. 

Q. Show that the points A(0, 7, 10), B(-1, 6, 6) and C(-4, 9, 6) form an isosceles right-angled triangle.

Q. Show that x^2 - 7x - 14(q^2 +1) =0 (q belongs to integers) has no integral root.

Q. If $P(\frac{1+t}{\sqrt{2}},\frac{2+t}{\sqrt{2}})$ be any point on a line, then the range of values of t for which the point P lies between the parallel lines x + 2y = 1 and 2x + 4y = 15, is

1. 
2. 
3. 
4. 

Q. The distance of the point (1, 2) from the line $3x+4y–5=0$ is units.

1. $\frac{6}{5}$
2. $\frac{5}{6}$
3. $\frac{16}{5}$

Q.

The points A$(-2,3,5),B(1,2,3)andC(7,0,-1)$ are _____

1. Collinear

2. Vertex of equilateral triangle

3. vertex of right angled isosceles triangle

4. vertex of right angle triangle

Q.

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

Q.

Three students are standing in a park with signboards 'SAVE ENVIRONMENT', 'DON'T LITTER' and 'KEEP YOUR PLACE CLEAN'. Their positions are marked by the points A(0, 7, 10), B(-1, 6, 6) and C(-4, 9, 6).

Three students are holdings green colour ribbon together. Does the ribbons form sides or a right angled triangle? Do you feel the need to promote?

What message is given from this question to the society?

Q. Show that the points A(0, 1, 2), B(2, -1, 3) and C(1, -3, 1) are vertices of an isosceles right angled triangle.

Q.

Find the coordinates of a point on y-axis which are at a distance of $5\sqrt{2}$ from the point $P(3,-2,5).$

Q.

Find the value of $a$, if the distance between the points $A(-3,-14)$ and $B(a,-5)$ is $9$ units.

Q.

The distance of (2, 3) from x+y=1 is

1. 2 units

2. 2√2 units

3. 4√2 units

4. 3√2 units

Q.

If $A\left(z_1\right),B\left(z_2\right),C\left(z_3\right)$ be the vertices of triangle ABC in which $|\underset{–}{ABC}$ = $\frac{\pi }{4}$ and $\frac{AB}{BC}$ = $\sqrt{2}$ then $z_2$ is equal to

1. 

2. 

3. 

4. 

Q.

The locus of a point P which moves in such a way that the segment OP, where O is the origin, has slope $\sqrt{3}$ is

1. 

2. 

3. 

4. 

Q.

Find the equation of the circle passing through the points (4, 1) and (6, 5) whose centre is on the line 4x + y = 16.

or

A rod of length 12 cm moves with its ends always touching the coordinate axes. Determine the equation of locus of point P on the rod, which is 3 cm from the end in contact with the X-axis.

Q. Find the point in yz-plane which is equidistant from the points A(3, 2, -1), B(1, -1, 0) and C(2, 1, 2).

Q.

The distance between the pair of points (7, 8) and (4, 2), if origin gets shifted to (1, -2), would be _________

1. 45

2. 3√5

3. √157

4. 3√3

Q.

If z lies on the curve |z| = 1 such that a $\le$ |z+1| + |1 + $z^2$ - z| $\le$ b then (a, b) can be

1. (1 , 3)

2. 

3. 

4. 

Q.

The equation of locus of a point where distance from the y-axis is equal to its distance from the point A(2, 1, -1) is-

1. $x^2+y^2+z^2=6$

2. $x^2-4x+2z+6=0$

3. $x^2+y^2-z^2=0$

4. $y^2-2y-4x+2z+6=0$

Q. If the vertices of A, B, C of a triangle ABC have position vectors (1, 2, 3), (-1, 0, 0) and (0, 1, 2) respectively then angle ABC equals

Q. distance between the points A(0, 7, 10) and C(–4, 9, 6) in space is .

1. 4
2. 5
3. 6
4. 8

Q.

A birdlover at $p(x,y,z)$ from a house watches two birds sitting on the branches of another tree at $A(2,5,8)$ and $B(3,7,2)$ such that AP=BP , show that $2x+4y-2z+31=0$