Find the equation of the locus of point such that the sun of the squares of its distances from A(3,0) and
B(-3,0) is four times the distance from A and B.
Can i get the answers ASAP??
Answers
Given : point such that the sum of the squares of its distances from A(3,0) and B(-3,0) is four times the distance from A and B.
To Find : Locus of the point
Solution:
Let say point is P is ( x , y )
Square of Distance from A ( 3 , 0) = (x - 3)² + ( y - 0)²
Square of Distance from B ( -3 , 0) = (x + 3)² + ( y - 0)²
Distance between A and B = √(3 + 3)² + (0 - 0)² = 6
Sum of the squares of its distances from A(3,0) and
B(-3,0) is four times the distance from A and B.
(x - 3)² + ( y - 0)² + (x + 3)² + ( y - 0)² = 4 * 6
=> x² - 6x + 9 + y² + x² + 6x + 9 + y² = 24
=> 2x² + 2y² + 18 = 24
=> x² + y² = 3
x² + y² = 3 is the locus of point such that the sum of the squares of its distances from A(3,0) and
B(-3,0) is four times the distance from A and B.
learn More:
Find the value of k, if the point P (-2, 2) lies on the locus x² - 7x + ky ...
brainly.in/question/7293046
Find The Equation Of The Locus Of A Point P The Square Of Whose ...
brainly.in/question/11144004