Question

if the distance of (p,4) from the point (5,0) is 5, find p.​

Answer 1

Step-by-step explanation:

let x1 =p, y1 =4 ,x2 = 5,y2 =0

(√[(y2 -y1)^2 + (x2 - x1)^2 ]= 5

√[(0-4)^2 + (5 - p)^2 ] = 5 --(1)

√( 16 + 25 + p^2 - 10p ] = 5

p^2 - 10p + 41 = 25

p^2 - 10p + 16 = 0

p^2 - 2p - 8p + 16 = 0

p( p - 2) - 8(p - 2) = 0

(p- 2) (p - 8) = 0 => p = 2,8

here p = (2,8) satisfies the equation(1),therefore possible values of P is 2 & 8 Answer

Answer 2

Answer:

✔p = 8 and 2

Step-by-step explanation:

✴If the distance of (p,4) from the point (5,0) is 5, find p.

➡Using Distance Formula

$\sqrt{x_2 - x_1}^2 + {y_2 - y_1}^2</h2><h2>$

$\sqrt{p-5}^2 + (4 - 0)^2</h2><h2>$=5

$(p-5)^2 + 16 = (5)^2$

$p^2 - 10p + 41= 25 .$

$p^2 -10p +16= 0$

$p^2 - 8p - 2p + 16 =0$

p(p - 8) - 2(p - 8)

(p - 2)(p - 8)=0

p = 2; p=8 Ans.