You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Condition of Concurrency of 3 Straight Lines

PM and PN are...

Question

PM and PN are the perpendiculars from any point P on the rectangular hyperbola xy = 8 to the asymptotes. If the locus of the mid point of MN is a conic, then the least distance of (1, 1) to director circle of the conic is

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B

OMPN is rectangle.

$P = (C t, \frac{c}{t})$

$M i d p o i n t = (\frac{c t}{2}, \frac{c}{2 t}) = (x, y) ∴ c y = \frac{c^{2}}{4} \Rightarrow e = \sqrt{2}$

Suggest Corrections

Similar questions

P M

and

P N

are the perpendiculars from any point

P

on the rectangular hyperbola

x y = 8

to the asymptotes. If the locus of the mid point of MN is a conic, then the least distance of

(1, 1)

to director circle of the conic is

P M

and

P N

are the perpendiculars from any point

P

on the rectangular hyperbola

x y = 8

to the asymptotes. If the locus of the mid point of MN is a conic, then the least distance of

(1, 1)

to director circle of the conic is

PM and PN are the perpendiculars from any point P on the rectangular hyperbola $x y = c^{2}$ to the asymptotes.

If the locus of the mid point of MN is a conic, then its eccentricity is

Q. If

P N

is the perpendicular from a point

P

on a rectangular hyperbola to its asymptotes, the locus of the mid-point of

P N

A_{1}

and

A_{2}

are the vertices of the conic

C_{1} : 4 (x - 3)^{2} + 9 (y - 2)^{2} - 36 = 0

and point

P

is moving in the plane such that

| P A_{1} - P A_{2} | = 3 \sqrt{2} .

Then the locus of

P

is another conic

C_{2} .

D_{1}

denotes the distance between foci of conic

C_{2},

D_{2}

denotes the product of perpendicular distances from the points

A_{1}

and

A_{2}

upon any tangent drawn to the conic

C_{2}

and

D_{3}

denotes length of tangent drawn from any point on the auxiliary circle of conic

C_{1}

to the auxiliary circle of the conic

C_{2},

then

{(\frac{D_{1} D_{2}}{D_{3}^{2}})}^{2}

is equal to

Join BYJU'S Learning Program

PM and PN are the perpendiculars from any point P on the rectangular hyperbola xy = 8 to the asymptotes. If the locus of the mid point of MN is a conic, then the least distance of (1, 1) to director circle of the conic is

The correct option is B OMPN is rectangle. P=(Ct,ct) Mid point=(ct2,c2t)=(x,y) ∴ cy=c24⇒e=√2

The correct option is B

OMPN is rectangle.

$P = (C t, \frac{c}{t})$

$M i d p o i n t = (\frac{c t}{2}, \frac{c}{2 t}) = (x, y) ∴ c y = \frac{c^{2}}{4} \Rightarrow e = \sqrt{2}$