Question

if a is equals to 1 to 20 equals to 2 - 3 and c is equals to minus 23 are the points a point p such that p a square + b square is equals to 2 PC square then show that the equation to the locus of p is 7 x minus 7 by + 4 is equal to zero​

Answer 1

Step-by-step explanation:

Let point P be (x,y)

Given A(1,2),B(2,−3),C(−2,3) and

PA

2 +PB 2 =2PC 2

⟹( (x−1) 2 +(y−2) 2 )2 ( (x−2) 2 +(y+3) 2 ) 2

=2( (x+2) 2 +(y−3) 2 ) 2

⟹x 2 +1−2x+y 2 +4−4y+x 2 +4−4x+y 2 +9+6y=2(x 2 +4+4x+y 2 +9−6y)

⟹2x 2 +2y 2 −6x+2y+18=2x 2 +2y 2 +8x−12y+26

⟹14x−14y+8=0

⟹7x−7y+4=0

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Answer 2

Step-by-step explanation:

Let point P be (x,y)

Given A(1,2) , B ( 2,-3 ) C ( -2,3 ) and PA² + PB² = 2PC²

= (√(x-1)² + (y-2)²)² + (√ (x-2)²+(y-3)²)² =

2(√(x+2)² + (y+3)²)²

= x² + 1 - 2 x + y² + 4 - 4y + x² + 4 - 4x + y² + 9 + 6y = 2(x² + 4 + 4x + y²+9 - 6y)

= 2x² + 2y² - 6x + 2y + 18 = 2x² + 2y² + 8x - 12y + 26

= 14x - 14y + 8 = 0

= 7x - 7y + 4 = 0

Therefore, the locus of point P is 7x - 7y + 5 = 0

$hope \: it \: helps \: you$