Write the general conic form equation of the locus of a point that moves so...

Question

that its distance from (-2, 3) equals its distance from the line x + 6 = 0

a. y² - 8x - 6y - 23 = 0

b.y² + 16x - 6y - 23 = 0

c.y² + 4x - 3y - 23 = 0

 

Answer 1

Let (x,y) be a point.

Distance between (-2,3) (x,y)

D = √[(x+2)^2+(y-3)^2]

Distance from the line x+6 = 0

These two distances are equal.

√[(x+2)^2+(y-3)^2] = x+6

(x+2)^2+(y-3)^2 = (x+6)^2

x^2+4+4x+y^2+9-6y = x^2+36+12x

Bring all the terms to left side.

x^2+4+4x+y^2+9-6y- x^2-36-12x

y^2-8x-6y-23 = 0

Option a is correct choice.