Pls give detailed steps Q 6 Find the equation of the curve formed by the set of all those - Maths - Introduction to Three Dimensional Geometry

Question

Pls give detailed steps
Q 6 Find the equation of the curve formed by the set of all those
points, the sum of whose distances from the points A(4, 0, 0) and
B(-4, 0, 0) as 10 units

Varun Rawat · Accepted Answer

Let Px,y,z be the point on the curve
Now, PA + PB = 10⇒x-42 + y2 + z2 + x+42 + y2 + z2 = 10⇒x-42 + y2 + z2 = 10 - x+42 + y2 + z2⇒x-42 + y2 + z2 = 100 + x+42 + y2 + z2 - 2 × 10 × x+42 + y2 + z2⇒x2 + 16 - 8x + y2 + z2 = 100 + x2 + 16 + 8x + y2 + z2 - 20x+42 + y2 + z2⇒-16x - 100= - 20x+42 + y2 + z2⇒4x + 25= 5x+42 + y2 + z2⇒16x2 + 625 + 200x = 25x2+16+8x + y2 + z2⇒16x2  + 200x + 625= 25x2 + 400 + 200x + 25y2 + 25z2⇒9x2 + 25y2 + 25z2  - 225 = 0

Pls give detailed steps Q.6. Find the equation of the curve formed by the set of all those points, the sum of whose distances from the points A(4, 0, 0) and B(-4, 0, 0) as 10 units.

Pls give detailed steps
Q.6. Find the equation of the curve formed by the set of all those points, the sum of whose distances from the points A(4, 0, 0) and B(-4, 0, 0) as 10 units.