Home
Class 12
MATHS
Prove that the locus of the point that m...

Prove that the locus of the point that moves such that the sum of the squares of its distances from the three vertices of a triangle is constant is a circle.

Text Solution

Verified by Experts

Let vertices of triangle are (0,0), (a,0) and (b,c).
The variable point (x,y) is such that
`(x-o)^(2)+(y-0)^(2)+(x-a)^(2)+(y-0)^(2)+(x-b)^(2)+(y-c)^(2)=lambda`(constant)
`:. 3x^(2)_3y^(2)-2(a+b)x-2cy+a^(2)+b^(2)+c^(2)-lambda=0`, which is equation of circle.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • CIRCLE

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 4.12|4 Videos

  • CIRCLE

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 4.13|4 Videos

  • CIRCLE

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 4.10|5 Videos

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise Matrix|4 Videos

  • CIRCLES

    CENGAGE ENGLISH|Exercise Comprehension Type|8 Videos

Similar Questions

Explore conceptually related problems

Prove that the locus of a point which moves such that the sum of the square of its distances from the vertices of a triangle is constant is a circle having centre at the centroid of the triangle.

The locus of a point which moves such that the sum of the squares of the distances from the three vertices of a triangle is constant, is a circle whose centre is at the:

The locus of a point which moves such that the sum of the square of its distance from three vertices of a triangle is constant is a/an circle (b) straight line (c) ellipse (d) none of these

Find the locus of the point such that the sum of the squares of its distances from the points (2, 4) and (-3, -1) is 30.

The locus of the point, for which the sum of the sqaures of distances from the coordinate axes is 25 is

A point moves so that the sum of the squares of its distances from two intersecting straight lines is constant. Prove that its locus is an ellipse.

The locus of a point which moves so that the difference of the squares of its distance from two given points is constant, is a

A point moves such that the sum of the squares of its distances from the sides of a square of side unity is equal to 9, the locus of such point is

Find the locus of appoint which moves such that the sum of the squares of its distance from the points A(1,2,3),B(2,-3,5)a n dC(0,7,4)i s120.

Find the locus of a pont which mioves such that the sum of the of its distances from points A(0,0-alpha) and B(0,0,alpha) is constant.

Home
Profile