Question

The distance of a point P from the straight line x=-4 is equal to its distance from the point (3,0). Find the equation to the locus of P.

Answer 1

Geometry

Given: the distance of the point P from the straight line c = - 4 is equal to its distance from the point (3, 0)

To find: the equation of the locus P

Solution: Let the coordinates of P are (p, q)

Then the distance of P from the straight line x = - 4 is

a₁ = | p + 4 | units

and the distance of P from (3, 0) is

a₂ = √{(p - 3)² + (q - 0)²} units

= √(p² - 6p + 9 + q²) units

By the given condition,

a₁ = a₂

or, | p + 4 | = √(p² - 6p + 9 + q²)

or, p² + 8p + 16 = p² - 6p + 9 + q²

or, q² = 14p + 7

Thus the required locus of P is

y² = 14x + 7

Answer: Required locus is y² = 14x + 7 .

Read more on Brainly.in

The equation to the locus of a point P for which the distance from P to (0,5) is double the distance from P to y-axis is...

- https://brainly.in/question/16753066