Question

find the equation of the locus of a point, the sum of whose distance from (0,2)and (0,-2)is 6​

Answer 1

Let Locus L(x,y) be any point on the locus and given points be A(0,2) and B(0,–2).

→ LA + LB = 6

→ √[(x–0)²+(y–2)²] + √[(x-0)²+(y+2)²] = 6

→ √[x²+(y–2)²] = 6–√[x²+(y+2)²]

→ x² +(y-2)² = 36 - 12√[x²+(y+2)²] + x² + (y+2)²

→ –8y–36 = –12√[x² + (y+2)²]

→ (2y+9) = 3√[x²+(y+2)²]

→ (2y + 9)² = 9(y² + (x + 2)²)

→ 4y² + 36y+81 = 9x²+9y²+36y+36

→ 9x² + 5y² = 45

Hence,

The Locus of the point will be 9x²+5y² = 45.