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Byju's Answer

Standard XII

Mathematics

Dot Product

A line drawn ...

Question

A line drawn through the point P (-1, 2) meets the hyperbola $x y = c^{2}$ at the points A and B (points A and B lie on same side of P) . Q is a point on AB such that PA, PQ and PB are in H.P then locus of Q is

x - 2 y = 2 c^{2}

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2 x - y = 2 c^{2}

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2 x + y + 2 c^{2} = 0

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x + 2 y + 2 c^{2}

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Solution

The correct option is B $2 x - y = 2 c^{2}$
Locus of Q is $S_{1} = 0$
$2 x - y = 2 c^{2}$

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Similar questions

A line drawn through the point $P (- 1, 2)$ meets the hyperbola $x y = c^{2}$ at the points $A$ and $B$ . (points $A$ and $B$ lie on same side of $P$ ) and $Q$ is a point on $A B$ such that $P A, P Q$ and $P B$ are in $H . P$ then locus of $Q$ is

A. $x - 2 y = 2 c^{2}$

B. $2 x - y = 2 c^{2}$

C. $x + 2 y = 2 c^{2}$

D. $2 x - y + 2 c^{2} = 0$

P

is the point

(- 1, 2)

, a variable line through

P

cuts the co-ordinate axes in

A

and

B

respectively.

Q

is a point on

A B

such that

P A, P Q

and

P B

are in

H . P .

Show that the locus of

Q

is the line

y = 2 x

Q. A line passing through the point

P (- 2, 3)

intersects the

x

and

y

axes at points

A

and

B

respectively. Let

Q

be a point on

A B

such that

P A, P Q,

and

P B

are in H.P, then the locus of point

Q

Q. A variable chord of circle

x^{2} + y^{2} = 4

is drawn from the point

P (3, 5)

meeting the circle at the point A and B. A point Q is taken on this chord such that

2 P Q = P A + P B

Locus of 'Q' is

Q. Suppose A, B are two points on

2 x - y + 3 = 0

and

P (1, 2)

is such that

P A = P B

. Then the midpoint of

A B

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A line drawn through the point P (-1, 2) meets the hyperbola xy=c2 at the points A and B (points A and B lie on same side of P) . Q is a point on AB such that PA, PQ and PB are in H.P then locus of Q is

The correct option is B 2x−y=2c2Locus of Q is S1=0 2x−y=2c2

A line drawn through the point P (-1, 2) meets the hyperbola $x y = c^{2}$ at the points A and B (points A and B lie on same side of P) . Q is a point on AB such that PA, PQ and PB are in H.P then locus of Q is

The correct option is B $2 x - y = 2 c^{2}$
Locus of Q is $S_{1} = 0$
$2 x - y = 2 c^{2}$