Home
Class 12
MATHS
Find the locus of a point, so that the j...

Find the locus of a point, so that the join of `(-5,1)` and `(3,2)` subtends a right angle at the moving point.

Text Solution

Verified by Experts

Lert P(k,h) be a moving point and let `A(-5,1)` and `B(3,2)` be the given points. From the given condition,we have `angle APB=90^@`
Therefore, `DeltaAPB` is a right-angled triangle, Hence,
`AB^2=AP^2+PB^2`
or `(3+5)^2+(2-1)^2=(h+5)^2+(k-1)^2+(h-3)^2+(k-2)^2`
or `65=2(h^2+k^2+2h-3k)+39`
or `h^2+k^2+2h-3k-13=0`
Hence, the locus of `(h,k)` is `x^2+y^2+2x-3y-13=0`.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • COORDINATE SYSYEM

    CENGAGE PUBLICATION|Exercise Illustration1.61|1 Videos

  • COORDINATE SYSYEM

    CENGAGE PUBLICATION|Exercise Illustration1.62|1 Videos

  • COORDINATE SYSYEM

    CENGAGE PUBLICATION|Exercise Illustration1.59|1 Videos

  • COORDINATE SYSTEM

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|2 Videos

  • CROSS PRODUCTS

    CENGAGE PUBLICATION|Exercise DPP 2.2|13 Videos

Similar Questions

Explore conceptually related problems

Find the condition If the segment joining the points (a,b) and (c,d) subtends a right angle at the origin

Find the locus of the mid point of the chord of the circle x^2+y^2=a^2 which subtend a right angle at the point (0,0).

Knowledge Check

  • The locus of the midpoints of chords of the circle x^(2) + y^(2) = 1 which subtends a right angle at the origin is

    A
    `x^(2) +y^(2) =(1)/(4)`
    B
    `x^(2) + y^(2) = (1)/(2)`
    C
    `xy = 0 `
    D
    `x^(2) - u^(2) = 0 `

    • Similar Questions

    Explore conceptually related problems

    Find the locus of the midpoint of the chords of the circle x^2+y^2-ax-by=0 which subtend a right angle at the point (a/2 ,b/2)dot is

    Find the locus of the midpoint of the chords of the parabola y^2=4ax .which subtend a right angle at the vertex.

    Find the locus of the middle points of the chords of the parabola y^2=4a x which subtend a right angle at the vertex of the parabola.

    The ratio of the distances of a moving point from the points (3,4) and (1,-2) is 2:3 , find the locus of the moving point.

    Find the locus of mid points of chords of the cirlce. x^(2)+y^(2)=a^(2) which subtend angle 90^(@) at the point (c,o).

    Find the locus of the point at which two given portions of the straight line subtend equal angle.

    Find the locus of a point which moves so that the sum of the squares of its distances from the points (3,0) and (-3,0) is always equal to 50.

    Home
    Profile