Let a and b be any two numbers satisfying 1 a 2 + 1 b 2 = 1 4 . Then, the foot of perpendicular from the origin on the variable line x a + y b = 1 lies on :

A hyperbola with each semi-axis = 2 .

A hyperbola with each semi-axis = 2

EASY

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The vertex of right angle of a right angled triangle lies on the straight line $2 x + y - 10 = 0$ and the two other vertices, at points $(2, - 3)$ and then the area of triangle in sq. units is :

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Important Questions on The Straight Line

EASY

Mathematics>Coordinate Geometry>The Straight Line>Straight Line and a Point

If the points

(2 a, a), (a, 2 a)

and

(a, a)

enclose a triangle of area

18

sq units, then the centroid of the triangle is equal to

HARD

Mathematics>Coordinate Geometry>The Straight Line>Straight Line and a Point

For $a > b > c > 0$ , the distance between $(1, 1)$ and the point of intersection of the lines $a x + b y + c = 0$ and $b x + a y + c = 0$ is less than $2 \sqrt{2}$ . Then

MEDIUM

Mathematics>Coordinate Geometry>The Straight Line>Straight Line and a Point

If the sum of distances from a point

P

on two mutually perpendicular straight lines is

1

unit, then the locus of

P

EASY

Mathematics>Coordinate Geometry>The Straight Line>Straight Line and a Point

The area of the triangle formed by the points

(a, b + c), (b, c + a), (c, a + b)

MEDIUM

Mathematics>Coordinate Geometry>The Straight Line>Straight Line and a Point

If the area of a triangle is

4

sq. units with vertices at

(- 2, 0), (0, 4)

and

(0, k)

, then the value of

k

MEDIUM

Mathematics>Coordinate Geometry>The Straight Line>Straight Line and a Point

Let

C

be the circle with centre

(0, 0)

and radius

3 unit

. The equation of the locus of the mid points of the chords of the circle

C

that subtend an angle of

\frac{2 π}{3}

at its centre, is:

EASY

Mathematics>Coordinate Geometry>The Straight Line>Straight Line and a Point

A line has slope

m

and

y

-intercept 4. The distance between the origin and the line is equal to

MEDIUM

Mathematics>Coordinate Geometry>The Straight Line>Straight Line and a Point

A point on the straight line,

3 x + 5 y = 15

which is equidistant from the coordinate axes will lie only in:

HARD

Mathematics>Coordinate Geometry>The Straight Line>Straight Line and a Point

The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices

(0, 0), (0, 41)

and

(41, 0)

MEDIUM

Mathematics>Coordinate Geometry>The Straight Line>Straight Line and a Point

Two sides of a parallelogram are along the lines,

x + y = 3

and

x - y + 3 = 0 .

If its diagonals intersect at

(2, 4),

then one of its vertex is:

HARD

Mathematics>Coordinate Geometry>The Straight Line>Straight Line and a Point

Let

a

and

b

be any two numbers satisfying

\frac{1}{a^{2}} + \frac{1}{b^{2}} = \frac{1}{4} .

Then, the foot of perpendicular from the origin on the variable line

\frac{x}{a} + \frac{y}{b} = 1

lies on :

HARD

Mathematics>Coordinate Geometry>The Straight Line>Straight Line and a Point

In a circle with centre

O

, suppose

A, P, B

are three points on its circumference such that

P

is the mid-point of minor arc

A B

. Suppose when

∠ A O B = θ, \frac{a r e a (Δ A O B)}{a r e a (Δ A P B)} = \sqrt{5} + 2

∠ A O B

is doubled to

2 θ,

then the ratio

\frac{a r e a (Δ A O B)}{a r e a (Δ A P B)}

is.

EASY

Mathematics>Coordinate Geometry>The Straight Line>Straight Line and a Point

A straight line through a fixed point

(2, 3)

intersects the coordinate axes at distinct points

P

and

Q

. If

O

is the origin and the rectangle

O P R Q

is completed, then the locus of

R

is:

EASY

Mathematics>Coordinate Geometry>The Straight Line>Straight Line and a Point

The area of a triangle is

5

sq units. Two of its vertices are

(2, 1)

and

(3, - 2)

.

The third vertex lies on

y = x + 3

,

then the coordinates of the third vertex can be

HARD

Mathematics>Coordinate Geometry>The Straight Line>Straight Line and a Point

2 x - y + 1 = 0

is a tangent to the hyperbola

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{16} = 1

, then which of the following CANNOT be sides of a right angled triangle?

HARD

Mathematics>Coordinate Geometry>The Straight Line>Straight Line and a Point

Let two points be

A (1, - 1)

and

B (0, 2) .

If a point

P (x^{'}, y^{'})

be such that the area of

∆ P A B = 5

sq. units and it lies on the line

3 x + y - 4 λ = 0,

then a value of

λ

EASY

Mathematics>Coordinate Geometry>The Straight Line>Straight Line and a Point

Suppose that the points

(h, k), (1, 2)

and

(- 3, 4)

lie on the line

L_{1} .

If a line

L_{2}

passing through the points

(h, k)

and

(4, 3)

is perpendicular to

L_{1},

then

\frac{k}{h}

equals:

HARD

Mathematics>Coordinate Geometry>The Straight Line>Straight Line and a Point

If a circle of radius

R

passes through the origin

O

and intersects the coordinate axes at

A

and

B

, then the locus of the foot of perpendicular from

O

A B

is :

MEDIUM

Mathematics>Coordinate Geometry>The Straight Line>Straight Line and a Point

Let the points of intersections of the lines

x - y + 1 = 0, x - 2 y + 3 = 0

and

2 x - 5 y + 11 = 0

are the mid points of the sides of a triangle

ABC .

Then the area of the triangle

ABC

MEDIUM

Mathematics>Coordinate Geometry>The Straight Line>Straight Line and a Point

Two points

A

and

B

with co-ordinates

(1, 1)

and

(- 2, 3)

are given respectively. Then, the locus of a point

P

so that the area of

Δ P A B

is 9 sq.units is given by _____

The vertex of right angle of a right angled triangle lies on the straight line 2x +y - 10 =0 and the two other vertices, at points (2, -3) and then the area of triangle in sq. units is :

Important Questions on The Straight Line

Learn and Prepare for any exam you want !

The vertex of right angle of a right angled triangle lies on the straight line $2 x + y - 10 = 0$ and the two other vertices, at points $(2, - 3)$ and then the area of triangle in sq. units is :