Mathematics Crash Course BITSAT>Chapter 8 - Point and Straight Line>Exercise 1>Q 81

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Mathematics

IMPORTANT

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The orthocenter of the triangle formed by the lines $x + y = 1$ and $2 y^{2} - x y - 6 x^{2} = 0$ is

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Important Questions on Point and Straight Line

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Mathematics

IMPORTANT

Mathematics Crash Course BITSAT>Chapter 8 - Point and Straight Line>Exercise 1>Q 1

The points

(1, 3)

and

(5, 1)

are the opposite vertices of a rectangle. The other two vertices lie on the line

y = 2 x + c,

then the value of

c

will be

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Mathematics

IMPORTANT

Mathematics Crash Course BITSAT>Chapter 8 - Point and Straight Line>Exercise 1>Q 2

Number of values of $α$ such that the points $(α, 6), (- 5, 0)$ and $(5, 0)$ form an isosceles triangle is

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Mathematics Crash Course BITSAT>Chapter 8 - Point and Straight Line>Exercise 1>Q 3

The line

x + y = 4

divides the line joining the points

(- 1, 1)

and

(5, 7)

in the ratio

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Mathematics

IMPORTANT

Mathematics Crash Course BITSAT>Chapter 8 - Point and Straight Line>Exercise 1>Q 4

The line

x + y = p

meets the

x

and

y

-axes at

A

and

B

, respectively. A triangle

A P Q

is inscribed in the triangle

O A B, O

being the origin, with right angle at

Q

.

P

and

Q

lie, respectively, on

O B

and

A B

. If the area of the triangle

A P Q

is

{(\frac{3}{8})}^{th}

of the area of the triangle

O A B,

then

\frac{A Q}{B Q}

is equal to

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Mathematics

IMPORTANT

Mathematics Crash Course BITSAT>Chapter 8 - Point and Straight Line>Exercise 1>Q 5

Let

A_{r}, r = 1, 2, 3 \dots . .

be points on the number line such that

O A_{1}, O A_{2}, O A_{3}, \dots . .

are in

G . P .

be a positive proper fraction. Let

M_{r}

be the middle point of the line segment

A_{r} A_{r + 1}

. Then the value of

\sum_{r = 1}^{\infty} O M_{r}

is equal to

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Mathematics

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Mathematics Crash Course BITSAT>Chapter 8 - Point and Straight Line>Exercise 1>Q 6

The middle point of the segment of the straight line joining the points

(p, q)

and

(q, - p)

is

(r / 2, s / 2) .

What is the length of the segment?

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Mathematics

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Mathematics Crash Course BITSAT>Chapter 8 - Point and Straight Line>Exercise 1>Q 7

A point

P

moves such that its distances from

(1, 2)

and

(- 2, 3)

are equal. Then the locus of

P

is

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Mathematics

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Mathematics Crash Course BITSAT>Chapter 8 - Point and Straight Line>Exercise 1>Q 8

The line

3 x + 4 y - 24 = 0

intersects the

X -

axis at

A

and

Y -

axis at

B .

Then, the circumcentre of the

△ O A B,

where

O

is the origin, is