Mathematics
Describe the locus of a point P, so that :
AB2 = AP2 + BP2,
where A and B are two fixed points.
Answer
We know that,
Angle subtended by a diameter on any point of a circle is 90°.
From figure,
By pythagoras theorem,
⇒ Hypotenuse2 = Perpendicular2 + Base2
⇒ AB2 = AP2 + BP2
We know that,
Pythagoras theorem applies on right angle triangle.
∴ AP ⊥ BP.
Hence, the locus of the point P is the circumference of a circle with AB as diameter.
Related Questions
Describe the locus of the centers of all circles passing through two fixed points.
Describe the locus of vertices of all isosceles triangles having a common base.
Describe the locus of a point in rhombus ABCD, so that it is equidistant from
(i) AB and BC.
(ii) B and D.
Describe :
(i) The locus of points at distances less than 3 cm from a given point.
(ii) The locus of points at distances greater than 4 cm from a given point.
(iii) The locus of points at distances less than or equal to 2.5 cm from a given point.
(iv) The locus of points at distances greater than or equal to 35 mm from a given point.
(v) The locus of the center of a given circle which rolls around the outside of a second circle and is always touching it.
(vi) The locus of the centers of all circles that are tangent to both the arms of a given angle.
(vii) The locus of the mid-points of all chords parallel to a given chord of a circle.
(viii) The locus of points within a circle that are equidistant from the end points of a given chord.