Question

If the sum of distances from a point P on two mutually perpendicular straight lines is 1 unit, then the locus of P is
(a) a parabola
(c) an ellipse
(b) a circle
(d) a straight line​

Answer 1

Answer:

$\huge\red{Answer}$

If the sum of distances from a point P on two mutually perpendicular straight lines is 1 unit, then the locus of P is

(a) a parabola

(c) an ellipse

(b) a circle

(d) a straight line

Correct option is D)

Answer 2

Answer:

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