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Q2. Whatever be the values of θ , prove that the locus of the point of intersection of the straight lines y =atan θ and asin 3 θ + ycos 3 θ = asin θ cos θ is a circle. Find the equation of the circle.


Q2. Whatever be the values of θ, prove that the locus of the point of intersection of the straight lines y =atanθ and asin3θ + ycos3θ = asinθcosθ  is a circle. Find the equation of the circle.


Grade:12

1 Answers

Aman Bansal
592 Points
10 years ago

Dear Arindam,

CONDITION 1 : A point moves such that it is always m units from the point Q.

Locus formed: A circle with centre Q and radius m.

 

  

 

Example :

Construct the locus of a point at a constant distance of 2 cm from a fixed point Q.

Solution:

Construct a circle with centre Q and radius 2 cm.

  

 

 

CONDITION 2 : A point P moves such that it is equidistant form two fixed pointsX and Y.

Locus formed: A perpendicular bisector of the line XY.

  

 

Example:

Construct the locus of point P moving equidistant from fixed points X and Y and XY= 6 cm.

Solution:

Construct a perpendicular bisector of the line XY.

  

 

 

CONDITION 3: A point P moves so that it is always m units from a straight lineAB.

Locus formed: A pair of parallel lines m units from AB.

 

  

 

Example:

Construct the locus of a point P that moves a constant distant of 2 cm from a straight line AB.

Solution:

Construct a pair of parallel lines 2 cm from AB.

  

 

 

CONDITION 4: A point moves so that it is always equidistant from two intersecting lines AB and CD.

Locus formed: Angle bisectors of angles between lines AB and CD.

 

 

Example:

The following figure shows two straight lines AB and CD intersecting at point O. Construct the locus of point P such that it is always equidistant from AB and CD.

  

 

Solution:

Construct angles bisectors of angles between lines AB and CD.

  

 

 

Best Of luck

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Thanks

Aman Bansal

Askiitian Expert

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