Mathematics Crash Course JEE Main>Chapter 22 - Point and Straight Line>Level 3>Q 7

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JEE Main

IMPORTANT

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If $P (1 + \frac{t}{\sqrt{2}}, 2 + \frac{t}{\sqrt{2}})$ be any point on a line, then the range of the values of $t$ for which the point $P$ lies between the parallel lines $x + 2 y = 1$ and $2 x + 4 y = 15$ is

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Important Questions on Point and Straight Line

MEDIUM

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 22 - Point and Straight Line>Level 3>Q 8

θ_{1}

and

θ_{2}

are the inclination of lines

L_{1}

and

L_{2}

with

x

-axis. If

L_{1}

and

L_{2}

pass through

P (x_{1}, y_{1})

, then equation of one of the angle bisector of these lines is

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 22 - Point and Straight Line>Level 3>Q 9

If the orthocenter of the triangle formed by the lines

2 x + 3 y - 1 = 0, x + 2 y + 1 = 0

and

a x + b y - 1 = 0

lies at origin, then

\frac{1}{a} + \frac{1}{b} =

MEDIUM

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 22 - Point and Straight Line>Level 3>Q 10

Let

C

be the centroid of the triangle with vertices

(3, - 1), (1, 3)

and

(2, 4) .

Let

P

be the point of intersection of the lines

x + 3 y - 1 = 0

and

3 x - y + 1 = 0 .

Then the line passing through the points

C

and

P

also passes through the point

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 22 - Point and Straight Line>Level 3>Q 11

Two pairs of straight lines with combined equations

x y + 4 x - 3 y - 12 = 0

and

x y - 3 x + 4 y - 12 = 0

form a square. Then the combined equation of its diagonals is