Question

please answer this question ​

Answer 1

Answer :

• Difference between x and y is 2.

Given :

• P(x , y) is equidistant from the points A(7 , 1) and B(3 , 5).

To Find :

• Relation between x and y.

Solution :

Here

are two points

• A(7 , 1)
• B(3 , 5)

Both are equidistant from P(x , y).

Then,

• AP = BP

Distance formula

• √[(x2 - x1)² + (y2 - y1)²]

★ Distance between AP

• x1 = 7
• x2 = x
• y1 = 1
• y2 = y

→ √[(x - 7)² + (y - 1)²]

★ Distance between BP

• x1 = 3
• x2 = x
• y1 = 5
• y2 = y

→ √[(x - 3)² + (y - 5)²

According to question :

→ √[(x - 7)² + (y - 1)²] = √[(x - 3)² + (y - 5)²]

→ (x - 7)² + (y - 1)² = (x - 3)² + (y - 5)²

→ x² + 49 - 14x + y² + 1 - 2y = x² + 9 - 6x + y² + 25 - 10y

→ 49 - 14x + 1 - 2y = 9 - 6x + 25 - 10y

→ 49 + 1 - 14x - 2y = 9 + 25 - 6x - 10y

→ 50 - 14x - 2y = 34 - 6x - 10y

→ 50 - 34 = - 6x + 14x - 10y + 2y

→ 16 = 8x - 8y

→ 8 (x - y) = 16

→ x - y = 16/8

→ x - y = 2

Hence, the relation between x and y is x - y = 2.

Answer 2

......Hope it helps......