Question

find the equation of the set of points P, the sum of whose distances from A(4,0,0)&B(-4,0,0) is equal to 10.

Answer 1

Namaskar Behna G ✌️✌️

आपके द्वारा पूछा गया प्रश्न का उत्तर ...दी गयी हुयी तस्वीर में है !!!!!!!!⬆️⬆️

आशा करते है आपको समझ आ गया होगा !!!!!❤️❤️

नहीं आया समझ तो कृपया दुबारा न तंग करे ✌️✌️✌️


❤️SAS❤️

Answer 2

Given:-

• The sum of distance from A(4,0,0) and B(-4,0,0) is equal to 10.

To find:-

• Find the equation..?

Solutions:-

• Let the coordinates of P be (x,y,z).

• The coordinates of point A and B are (4,0,0) and (-4,0,0).

Given that, PA + PB = 10

=> √(x - 4)² + y² + z² + √(x - 4)² + y² + z² = 10

=> √(x - 4)² + y² + z² = 10 - √(x - 4)² + y² + z²

On squaring both sides, we obtain.

=> (x - 4)² + y² + z² = 100 - 20√(x + 4)² + y² + z² + (x + 4)² + y² + z²

=> x² - 8x + 16 + y² + z² = 100 - 20 √x² + 8x + 16 + y² + z²

=> 20 √x² + 8x + 16 + y² + z² = (25 + 4x)

On squaring both sides again, we obtain.

=> 25(x² + 8x + 16 + y² + z²) = 625 + 16x² + 200x

=> 25x² + 200x + 400 + 25y² + 25z²) = 625 + 16x² + 200x

=> 9x² + 25y² + 25z² - 225 = 0

Hence, the required equation is 9x² + 25y² + 25z² - 225 = 0.