Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 85

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IMPORTANT

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The orthocenter of the triangle formed by the lines $x y = 0$ and $x + y = 1$ is

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Important Questions on Coordinates and Straight Lines

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JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 86

If

α_{1}, α_{2}, α_{3}, β_{1}, β_{2}, β_{3}

are the values of

n

for which

\sum_{r = 0}^{n - 1} x^{2 r}

is divisible by

\sum_{r = 0}^{n - 1} x^{r}

, then the triangle having vertices

(α_{1}, β_{1}), (α_{2}, β_{2})

and

(α_{3}, β_{3})

cannot be

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Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 87

The straight lines

x + y = 0, 3 x + y - 4 = 0, x + 3 y - 4 = 0

form a triangle which is

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Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 88

All points lying inside the triangle formed by the points

(1, 3), (5, 0)

and

(- 1, 2)

satisfy

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IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 89

The equations of a pair of opposite sides of a parallelogram are

x^{2} - 5 x + 6 = 0

and

y^{2} - 6 y + 5 = 0

. The equations of its diagonals are

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Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 1

The equation(s) of the straight line(s), inclined at

30 °

to the

x

-axis such that the length of its (each of their) line segment(s) between the co-ordinate axes is

10 units

, is (are)

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Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 2

A ray of light travelling along the line

x + y = 1

is incident on the

x

-axis and after refraction it enters the other side of the

x

-axis by turning

30 °

away from the

x

-axis. The equation of the line along which the refracted ray travels is

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Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 3

A ray travelling along the line

3 x - 4 y = 5

after being reflected from a line

L

travels along the line

5 x + 12 y = 13

. Then the equation of the line

L

is

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JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 4

A (1, 2)

and

B (7, 10)

are two points. If

P (x, y)

is a point such that the angle

A P B

is

60 °

and the area of the triangle

A P B

is maximum, then which of the following is (are) true?