Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-2>Q 47

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$A \equiv (4, 2)$ and $B \equiv (2, 4)$ are two given points and a point $P$ on the line $3 x + 2 y + 10 = 0$ is given then which of the following is/are true.

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Important Questions on Point and Straight Line

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-2>Q 48

A line passing through

P = (\sqrt{3}, 0)

and making an angle of

60 °

with positive direction of

x

- axis cuts the parabola

y^{2} = x + 2

at

A

and

B

, then :

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-2>Q 49

Let

u \equiv a x + b y + a \sqrt[3]{b} = 0, v \equiv b x - a y + b \sqrt[3]{b} = 0,

where

a, b \in R

be two straight lines, then find the equations of the bisectors of the angles formed by

k_{1} u - k_{2} v = 0 & k_{1} u + k_{2} v = 0

for non zero real

k_{1} & k_{2}

.

HARD

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-2>Q 50

The sides of a triangle are the straight lines

x + y = 1, 7 y = x

and

\sqrt{3} y + x = 0

, then which of the following is an interior point of the triangle?

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-2>Q 51

The line

l_{1}

passing through the point

(1, 1)

and the

l_{2}

passes through the point

(- 1, 1)

. If the difference of the slope of lines is

2 .

Find the locus of the point of intersection of the

l_{1}

and

l_{2}

.

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-2>Q 52

The two lines pairs

y^{2} - 4 y + 3 = 0

and

x^{2} + 4 x y + 4 y^{2} - 5 x - 10 y + 4 = 0

enclose a

4

sided convex polygon, then the correct statement among the following is/are

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-2>Q 53

If the distance between the lines represented

9 x^{2} - 24 x y + 16 y^{2} + k (6 x - 8 y) = 0

is

4,

then

k

may be

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-2>Q 54

Coordinates of the vertices

B

and

C

of a triangle

A B C

are

(2, 0)

and

(8, 0)

, respectively. The vertex

A

is varying in such a way that

4 \tan \frac{B}{2} \cdot \tan \frac{C}{2} = 1 .

Then locus of

A

is

EASY

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-3>Q 1

The number of complex numbers

z

such that

| z - 1 | = | z + 1 | = | z - i |

equals