find the equation of locus of a point which is at a distance 5 from A(4,-3).
Answers
Step-by-step explanation:
answer is given above and
Therefore the equation of locus of a point which is at a distance of 5 units from A( 4, -3 ) is 'x² + y² - 8x + 6y = 0'
Given:
The point A = ( 4, -3 )
To Find:
The equation of locus of a point is at a distance of 5 units from point A( 4,-3 ).
Solution:
The given question can be solved as shown below.
We have to find an equation that has the distance between point A and all the points lying on the equation as 5 units.
So it is the circle with a center at A( 4,-3 ) and a radius of 5 units.
Equation of circle ⇒ ( x - h )² + ( y - k )² = r²
where ( h,k ) are the coordinates of the center that is ( 4,-3 ) and r = radius of the circle = 5 units.
⇒ ( x - 4 )² + ( y - ( -3 ) )² = 5²
⇒ ( x - 4 )² + ( y + 3 )² = 5²
⇒ x² + 16 - 8x + y² + 9 + 6y = 25
⇒ x² + y² - 8x + 6y + 9 + 16 = 25
⇒ x² + y² - 8x + 6y + 25 = 25
⇒ x² + y² - 8x + 6y = 0
Therefore the equation of locus of a point which is at a distance of 5 units from A( 4, -3 ) is 'x² + y² - 8x + 6y = 0'
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