Beta Question Bank for Engineering: Mathematics>Chapter 16 - Point and Straight Line>EXERCISE-1>Q 34

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If one diagonal of a square is along the line $x = 2 y$ and one of its vertex is $(3, 0)$ , then its sides through this vertex are given by the equations-

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Important Questions on Point and Straight Line

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Beta Question Bank for Engineering: Mathematics>Chapter 16 - Point and Straight Line>EXERCISE-1>Q 35

The line

(p + 2 q) x + (p - 3 q) y = p - q

for different values of

p

and

q

passes through a fixed point whose co-ordinates are-

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Beta Question Bank for Engineering: Mathematics>Chapter 16 - Point and Straight Line>EXERCISE-1>Q 36

The equation

2 x^{2} + 4 x y - p y^{2} + 4 x + q y + 1 = 0

will represent two mutually perpendicular straight lines, if-

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Beta Question Bank for Engineering: Mathematics>Chapter 16 - Point and Straight Line>EXERCISE-1>Q 37

Equation of the pair of straight lines through origin and perpendicular to the pair of straight lines

5 x^{2} - 7 x y - 3 y^{2} = 0

is

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Beta Question Bank for Engineering: Mathematics>Chapter 16 - Point and Straight Line>EXERCISE-1>Q 38

If the straight lines joining the origin and the points of intersections of the curve

5 x^{2} + 12 x y - 6 y^{2} + 4 x - 2 y + 3 = 0

and

x + k y - 1 = 0

are equally inclined to the co-ordinate axis, then the value of

k

-

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Beta Question Bank for Engineering: Mathematics>Chapter 16 - Point and Straight Line>EXERCISE-2>Q 1

The graph of the function

\cos x \cos (x + 2) - \cos^{2} (x + 1)

is-

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Beta Question Bank for Engineering: Mathematics>Chapter 16 - Point and Straight Line>EXERCISE-2>Q 2

If

x, y

and

z

are the distances of in-centre from the vertices of the triangle

A B C

, respectively, then

\frac{a b c}{x y z}

is

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Beta Question Bank for Engineering: Mathematics>Chapter 16 - Point and Straight Line>EXERCISE-2>Q 3

The medians of a

∆ A B C

are

9 cm, 12 cm

and

15 cm

, respectively. Then the area of the triangle is

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Beta Question Bank for Engineering: Mathematics>Chapter 16 - Point and Straight Line>EXERCISE-2>Q 4

In an isosceles

∆ A B C

, if the altitudes intersect on the inscribed circle then the cosine of the vertical angle

' A'

is