Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 42

EASY

JEE Main/Advance

IMPORTANT

Earn 100

Prove that the circumcentre, orthocentre, incentre & centroid of the triangle formed by the points $A (- 1, 11); B (- 9, - 8); C (15, - 2)$ are collinear, without actually finding any of them.

Important Questions on Point and Straight Line

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 43

Find the locus of centroid of

A B = A C,

if line

A B

passes through

(3, 2), A

and

B

are on coordinate axes.

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 44

Find the locus of the centroid of a triangle whose vertices are

(a \cos t, a \sin t), (b \sin t, - b \cos t)

and

(1, 0)

where

' t'

is the parameter.

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 45

Show that equation of the locus of a point which moves so that difference of its distance from two given points

(a e, 0)

and

(- a e, 0)

is equal to

2 a

is

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{a^{2} (e^{2} - 1)} = 1 .

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 46

Find the locus of point of intersection of the lines

x \cos α + y \sin α = a

and

x \sin α - y \cos α = b,

where

α

is a parameter.

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 47

The area of the triangle formed by the intersection of a line parallel to

x -

axis and passing through

P (h, k)

with the lines

y = x

and

x + y = 2

is

4 h^{2}

. Find the locus of the point

P

.

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 48

Find equations of acute and obtuse angle bisectors of the angle between the lines

4 x + 3 y - 7 = 0

and

24 x + 7 y - 31 = 0 .

Also comment in which bisector origin lies.

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 49

Find the equation of a straight line passing through the point

(4, 5)

and equally inclined to the lines

3 x = 4 y + 7

and

5 y = 12 x + 6 .

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 50

The line

x + 3 y - 2 = 0

bisects the angle between a pair of straight lines of which one has equation

x - 7 y + 5 = 0,

then find equation of other line.