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Figures Formed When Parallels Cut

93. A variabl...

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{ 93. A variable line }L is drawn through }O(0,0) to meet lines }}{L_1:2x+3y=5 and }L_2:2x+3y=10 at point }P and }Q,}{ respectively. A point }R is taken on }L such that }2OP\cdot OQ}{=OR\cdot OP+OR\cdot OQ. Locus of }R is

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Q. A variable line

L

is drawn through

O (0, 0)

to meet the lines

L_{1} : y - x - 10 = 0

L_{2} : y - x - 20 = 0

A

B

respectively. A point

P

L

\frac{2}{O P} = \frac{1}{O A} + \frac{1}{O B}

P, A, B

lies on same side of origin

O

P

Q. A variable line

L

is drawn through

O (0, 0)

L_{1} : x - y - 8 = 0

L_{2} : x - y - 16 = 0

A

B

respectively. A point

P

L

\frac{1}{4 O P} = \frac{1}{O A} + \frac{1}{O B}

. Then the locus of

P

Q. A variable line

L

is drawn through

O (0, 0)

L_{1} : x - y - 8 = 0

L_{2} : x - y - 16 = 0

A

B

respectively. A point

P

L

\frac{1}{4 O P} = \frac{1}{O A} + \frac{1}{O B}

. Then the locus of

P

Q. A variable line

L

is drawn through

O (0, 0)

to meet the lines

L_{1} : x + 2 y - 3 = 0

L_{2} : x + 2 y + 4 = 0

M

N

respectively. A point

P

is taken on line

L

\frac{1}{O P^{2}} = \frac{1}{O M^{2}} + \frac{1}{O N^{2}}

. Then the locus of

P

Q. A straight line

L

through the origin meets the line

x + y = 1

x + y = 3

P

Q

respectively.Through

P

Q

two straight lines

L_{1}

L_{2}

aredrawn, parallel to

2 x - y = 5

3 x + y = 5

respectively. Lines

L_{1}

L_{2}

R

. Show that the locus of

R

L

varies, is a straight line.

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