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If the curve $x^{2} + 2 y^{2} = 2$ intersects the line $x + y = 1$ at two points $P$ and $Q$ , then the angle subtended by the line segment $P Q$ at the origin is

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Important Questions on Point and Straight Line

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 22 - Point and Straight Line>Level 2>Q 20

Let the equation of the pair of lines,

y = p x

and

y = q x,

can be written as

(y - p x) (y - q x) = 0 .

Then the equation of the pair of the angle bisectors of the lines

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

is:

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Mathematics Crash Course JEE Main>Chapter 22 - Point and Straight Line>Level 3>Q 1

The line

x + y = p

meets the

x

and

y

-axes at

A

and

B

, respectively. A triangle

A P Q

is inscribed in the triangle

O A B, O

being the origin, with right angle at

Q

P

and

Q

lie, respectively, on

O B

and

A B

. If the area of the triangle

A P Q

{(\frac{3}{8})}^{th}

of the area of the triangle

O A B,

then

\frac{A Q}{B Q}

is equal to

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Mathematics Crash Course JEE Main>Chapter 22 - Point and Straight Line>Level 3>Q 2

Let

A_{r}, r = 1, 2, 3 \dots . .

be points on the number line such that

O A_{1}, O A_{2}, O A_{3}, \dots . .

are in

G . P .

be a positive proper fraction. Let

M_{r}

be the middle point of the line segment

A_{r} A_{r + 1}

. Then the value of

\sum_{r = 1}^{\infty} O M_{r}

is equal to

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

Let

A B C

be a fixed triangle and

P

be a variable point in the plane of triangle

A B C .

Suppose

a, b, c

are lengths of sides

B C, C A and A B

are opposite to angles

A, B and C,

respectively. If

a {(P A)}^{2} + b {(P B)}^{2} + c {(P C)}^{2}

is minimum, then point

P

with respect to

∆ A B C

is the

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Mathematics Crash Course JEE Main>Chapter 22 - Point and Straight Line>Level 3>Q 4

If $A B C D$ is a $2 \times 2$ square, $E$ is the midpoint of $\bar{A B}, F$ is the midpoint of $\bar{B C}, \bar{A F}$ and $\bar{D E}$ intersect at $I$ and $B D$ and $A F$ intersect at $H$ and the area of the quadrilateral $B E I H$ is $\frac{k}{2 k + 1}$ , find $k .$

Question Image

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Mathematics Crash Course JEE Main>Chapter 22 - Point and Straight Line>Level 3>Q 5

A line through

A (- 5, - 4)

meets the lines

x + 3 y + 2 = 0, 2 x + y + 4 = 0

and

x - y - 5 = 0

B, C

and

D

respectively. if

{(\frac{15}{AB})}^{2} + {(\frac{10}{AC})}^{2} = {(\frac{6}{AD})}^{2},

then the equation of the line is

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 22 - Point and Straight Line>Level 3>Q 6

The equation of the straight line in the normal form which is parallel to the lines

x + 2 y + 3 = 0

and

x + 2 y + 8 = 0

and dividing the distance between these two lines in the ratio

1 : 2

internally is

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

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

If the curve x2+2y2=2 intersects the line x+y=1 at two points P and Q, then the angle subtended by the line segment PQ at the origin is

Important Questions on Point and Straight Line

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If the curve $x^{2} + 2 y^{2} = 2$ intersects the line $x + y = 1$ at two points $P$ and $Q$ , then the angle subtended by the line segment $P Q$ at the origin is