Home
Class 12
MATHS
Through a fixed point (h, k) secants are...

Through a fixed point (h, k) secants are drawn to the circle `x^(2) + y^(2) =a^(2)` . The locus of the mid points of the secants intercepted by the given circle is

A

`2(x^(2)+y^(2))=hx+ky`

B

`x^(2)+y^(2)=hx+ky`

C

`x^(2)+y^(2)+hx+ky=0`

D

`x^(2)+y^(2)-hx+ky+13=0`

Text Solution

Verified by Experts

The correct Answer is:
B
Let mid point of the chord be `P(x_(1),y_(1))`
`:.` Equation of chord `S_(1)=T`
`x_(1)^(2)+y_(1)^(2)-a^(2)="xx"_(1)+"yy"_(1)-a^(2)`
This chord passes through (h,k)
`x_(1)^(2)+y_(1)^(2)=hx_(1)+ky_(1)" ":." "` Locus of `P(x_(1),y_(1))` be `x_(1)^(2)+y_(1)^(2)=hx_(1)+ky_(1)`
Promotional Banner

Similar Questions

Explore conceptually related problems

Through a fixed point (h,k) secants are drawn to the circle x^(2)+y^(2)=r^(2). Then the locus of the mid-points of the secants by the circle is

Through a fixed point (h,k), secant are drawn to the circle x^(2)+y^(2)=r^(2) . Show that the locus of the midpoints of the secants by the circle is x^(2)+y^(2)=hx+ky .

From (3,4) chords are drawn to the circle x^(2)+y^(2)-4x=0. The locus of the mid points of the chords is :

If tangents are drawn to the ellipse 2x^(2) + 3y^(2) =6 , then the locus of the mid-point of the intercept made by the tangents between the co-ordinate axes is

From the origin,chords are drawn to the circle (x-1)^(2)+y^(2)=1. The equation of the locus of the mid-points of these chords is circle with radius