Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-3>Q 19

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Let $a, b, c$ and $d$ be non-zero numbers. If the point of intersection of the lines $4 a x + 2 a y + c = 0$ and $5 b x + 2 b y + d = 0$ , lies in the fourth quadrant and is equidistant from the two axes, then

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Important Questions on Point and Straight Line

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-3>Q 20

The number of points having both coordinates as integers that lie in the interior of the triangle with vertices

(0, 0), (0, 41)

and

(41, 0),

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-3>Q 21

Two sides of a rhombus are along the lines,

x - y + 1 = 0

and

7 x - y - 5 = 0 .

If its diagonals intersect at

(- 1, - 2)

, then which one of the following is a vertex of this rhombus?

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-3>Q 22

Let

k

be an integer such that the triangle with vertices

(k, - 3 k), (5, k)

and

(- k, 2)

has area

28

square units. Then, the orthocentre of this triangle is at the point

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-3>Q 24

Consider the set of all lines

p x + q y + r = 0

such that

3 p + 2 q + 4 r = 0 .

Which one of the following statements is true?

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-3>Q 25

Let the equations of two sides of a triangle be

3 x - 2 y + 6 = 0

and

4 x + 5 y - 20 = 0

If the orthocentre of this triangle is at

(1, 1)

then the equation of its third side is

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-3>Q 26

Two vertices of a triangle are

(0, 2)

and

(4, 3) .

If its orthocenter is at the origin, then its third vertex lies in which quadrant?

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-3>Q 27

Locus of the image of the point

(2, 3)

in the line

(2 x - 3 y + 4) + k (x - 2 y + 3) = 0, k \in R,

is a

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-3>Q 28

Let the orthocentre and centroid of a triangle be

A (- 3, 5)

and

B (3, 3)

. respectively. If

C

is the circumcentre of this triangle, then the radius of the circle having line segment

A C

as diameter, is