Coordinate Geometry

Q. Find the area enclosed by the equation |x| + |y| = 4.

1. 4 squnits
2. 8 squnits
3. 16 squnits
4. 32 squnits

Q.

The centroid of the triangle formed by the pair of straight lines $12x^2-20xy+7y^2=0$ and the line $2x-3y+4=0$ is

1. $\left(\frac{-7}{3},\frac{7}{3}\right)$

2. $\left(\frac{8}{3},\frac{8}{3}\right)$

3. $\left(\frac{-8}{3},\frac{8}{3}\right)$

4. $\left(\frac{4}{3},\frac{4}{3}\right)$

Q. Orthocentre of the triangle whose sides are given by 4x - 7y + 10 = 0, x + y - 5 = 0 & 7x + 4y - 15 = 0 is

1. (1, - 2)
2. (-1, -2)
3. (-1, 2)
4. (1, 2)

Q. ABCD is a rhombus with the diagonals AC and BD intersecting at the origin on the x y plane. The equation of the straight line AD is x + y =1. What is the equation of BC? (CAT 2000)

1. x + y = 1
2. None of these
3. x – y = -1
4. x + y = -1

Q. Find the equation of circle whose radius is 5 and which touches the circle $x^2+y^2-2x-4y-20=0$ at the point (5, 5).

1. x² + y² + 6x – 3y - 54 =0
2. x² + y² – 18x – 8y + 60 =0
3. x² + y² – 18x – 16y + 120 =0
4. x² + y² – 17x – 19y + 50 =0

Q. The coordinates of the diagonals of a square are (2, 0) and (0, 5). What is the area of the square?

1. $\frac{\sqrt{29}}{\sqrt{2}}sq.units$
2. $29sq.units$
3. $\frac{29}{4}sq.units$
4. $14.5sq.units$

Q. The area enclosed by 2|x| + 3|y| = 6 is (in sq.units)___

Q. Which one of the following points on the line 2x - 3y = 5 is equidistant from (1, 2) and (3, 4)?

1. (7, 3)
2. (4, 1)
3. (1, -1)
4. (-2, -3)

Q.

The equation of the straight line joining the origin to the point of intersection of $y-x+7=0$ and $y+2x-2=0$ is

1. $3x+4y=0$

2. $3x-4y=0$

3. $4x-3y=0$

4. $4x+3y=0$

Q. Consider a triangle drawn on the X – Y plane with its three vertices at (41, 0), (0, 41) and (0, 0), each vertex being represented by its (X, Y) coordinates. The number of points with integer coordinates inside the triangle (excluding all the points on the boundary) is (CAT 2005)

1. 780
2. 800
3. 820
4. 741

Q. Find the equations of the bisectors of the angle between the straight line 3x + 4y + 2 = 0 and 5x - 12 y - 6 = 0.

1. 8x + y + 7 = 0
2. 16x - 2y - 1 = 0
3. x + 8y + 4 = 0
4. both (b) and (c)

Q.

A straight line $\frac{x}{a}-\frac{y}{b}=1$ passes through the point (8, 6) and cuts off a triangle of area 12 units from the axes of coordinates. Find the equations of the straight line.

1. 4x - 3y =12

2. 3x - 2y = 12

3. 3x - 8y + 24 = 0

4. both (a) and (c)

Q. Find the equation of the line on which length of the perpendicular from the origin is 5 and the angle which this perpendicular makes with the x-axis is ${60}^{\circ }$.

1. none of (a), (b), (c)
2. $x\sqrt{3}+2y+8=0$
3. $x+\sqrt{2}y-7=0$
4. $x+\sqrt{3}y=10$

Q.

Find the area of quadrilateral formed by joining the points (-4, 2), (1, -1)(4, 1) and (2, 5):

1. 24.5

2. 25.4

3. 20.5

4. none of these

Q.

If $2x-4y=9$ and $6x-12y+7=0$ are common tangents to the circle, then radius of circle is

1. $\frac{\surd 3}{5}$

2. $\frac{17}{6\surd 5}$

3. $\frac{\surd 2}{3}$

4. $\frac{17}{3\surd 5}$

Q. Three points A (1, -2), B(3, 4) and C(4, 7) form:

1. a straight line
2. an equilateral triangle
3. a right angled triangle
4. none of (a), (b), (c)

Q.

In $∆ABC$, if $A\left(3,5\right)$, $B\left(7,8\right)$ and $C\left(1,-10\right)$, then find the equation of the median through $A$.

Q. Three points A, B and C are collinear such that AB = 2BC. If the coordinates of the points A and B are (1, 7) and (6, -3) respectively, then the coordinates of the point C can be

1. 
2. 
3. 
4. 

Q. The points (p - 1, p+2), (p, p+1), (p+1, p) are collinear for

1. p = 0
2. p = 1
3. p = - 1 / 2
4. Any value of p

Q. Find the equation of the straight line which passes through the point of intersection of the straight lines 3x - 4y + 1 = 0 and 5x + y - 1 = 0 and cuts off equal intercepts from the axis.

1. 23x + 23y = 11
2. 9x + 18y + 5 = 0
3. None of these
4. 32x + 32y + 11 = 0

Q. If the middle points of the sides of a triangle be (-2, 3), (4, -3) and (4, 5), then the centroid of the triangle is:

1. (5/3, 2)
2. (5/6, 1)
3. (2, 5/3)
4. (1, 5/6)

Q.

The area of the triangle formed by the lines ${\mathrm{x}}^2-{4\mathrm{y}}^2=0$ and $\mathrm{x}=\mathrm{a}$, is

1. ${2\mathrm{a}}^2$

2. $\frac{a^2}{2}$

3. $\frac{\sqrt{3}{a}^2}{2}$

4. $\frac{2a^2}{\sqrt{3}}$

Q. Determine the radius of the circle, two of whose tangents are the lines 2x+3y-9 = 0 and 4x+6y+19 =0

1. 
2. 
3. 
4. 

Q.

The points (2, 5) and (6, 3) are two end points of a diagonal of a rectangle. If the other diagonal has the equation y = 3x + c, then c is

1. -5

2. -7

3. -8

4. -6

Q.

The area of the closed region bounded by the equation $|x|+|y|=2$ in the two-dimensional plane is

1. $4\pi$

2. $8$

3. $2\pi$

4. $4$

Q. Two sides of rhombus ABCD are parallel to the lines y = x + 2 and y = 7x + 3. If the diagonal of rhombus intersect at the point (1, 2) and the vertex A lies on y-axis find the possible co-ordinates of A.

Q. Find the equation of the straight line which passes through the point of intersection of the straight lines x + y = 8 and 3x - 2y + 1 = 0 and is parallel to the straight line joining the points (3, 4) and (5, 6).

1. x - y + 2 = 0
2. 3x - 4y + 8 = 0
3. none of these
4. x + y - 2 = 0

Q. Find the equation of circle whose radius is 5 and which touches the circle x² +y² – 2x – 4y – 20 =0 at the point (5, 5).

1. x² + y² + 6x – 3y - 54 =0
2. x² + y² – 18x – 16y + 120 =0
3. x² + y² – 17x – 19y + 50 =0
4. x² + y² – 18x – 8y + 60 =0

Q. Find the equation of the line which passes through the point of intersection of the lines 2x - y + 5 = 0 and 5x + 3y - 4 = 0 and is perpendicular to the line x - 3y + 21 = 0

1. 2x + y + 8 = 0
2. 3x+ 4y - 7 = 0
3. 3x+ y = 0
4. none of these

Q. Find the distance between two parallel lines 5x +12y - 30 = 0 and 5x +12y-4=0

1. 7
2. $\frac{5}{2}$
3. 2
4. 3