हिंदी

Describe the locus of a point P, so that: AB2 = AP2 + BP2, where A and B are two fixed points. - Mathematics

Advertisements
Advertisements

प्रश्न

Describe the locus of a point P, so that:

AB2 = AP2 + BP2,

where A and B are two fixed points.

आकृति
Advertisements

उत्तर

 
The locus of the point P is the circumference of a circle with AB as diameter and satisfies the condition AB2 = AP2 + BP2

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Use graph paper for this question. Take 2 cm = 1 unit on both the axes.

  1. Plot the points A(1, 1), B(5, 3) and C(2, 7).
  2. Construct the locus of points equidistant from A and B.
  3. Construct the locus of points equidistant from AB and AC.
  4. Locate the point P such that PA = PB and P is equidistant from AB and AC.
  5. Measure and record the length PA in cm. 

AB and CD are two intersecting lines. Find a point equidistant from AB and CD, and also at a distance of 1.8 cm from another given line EF. 


A and B are fixed points while Pis a moving point, moving in a way that it is always equidistant from A and B. What is the locus of the path traced out by the pcint P? 


In given figure, ABCD is a kite. AB = AD and BC =CD. Prove that the diagona AC is the perpendirular bisector of the diagonal BD. 


In Δ PQR, bisectors of  ∠ PQR and ∠ PRQ meet at I. Prove that I is equidistant from the three sides of the triangle , and PI bisects ∠ QPR . 


Draw and describe the locus in the following case:

The locus of points inside a circle and equidistant from two fixed points on the circle.


Use ruler and compass only for the following question. All construction lines and arcs must be clearly shown.

  1. Construct a ΔABC in which BC = 6.5 cm, ∠ABC = 60°, AB = 5 cm.
  2. Construct the locus of points at a distance of 3.5 cm from A.
  3. Construct the locus of points equidistant from AC and BC.
  4. Mark 2 points X and Y which are at a distance of 3.5 cm from A and also equidistant from AC and BC. Measure XY.

State and draw the locus of a point equidistant from two given parallel lines.


Using a ruler and compass only: 
(i) Construct a triangle ABC with BC = 6 cm, ∠ABC = 120° and AB = 3.5 cm.
(ii) In the above figure, draw a circle with BC as diameter. Find a point 'P' on the circumference of the circle which is equidistant from Ab and BC.
Measure ∠BCP.


How will you find a point equidistant from three given points A, B, C which are not in the same straight line?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×