Question

The distance of point P(x, y) from the origin is 5 units, then the coordinates of point ‘P’ are)

Answer 1

Answer:

distance formula

Step-by-step explanation:

substitution method

Answer 2

Any points satisfying the equation $x^2+y^2=25$ is the coordinates of P

Step-by-step explanation:

• Given that the distance of point P(x, y) from the origin is 5 units
• That is the distance between the point P(x,y) and (0,0) is 5 units
• Distance s=5 units

To find the coordinate of the point P :

• Let $(x_1,y_1)$ be the point P(x,y)and $(x_2,y_2)$ be the point (0,0)

Now by distance formula  we have that

$s=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ units

• Substitute the points and distance in the formula we get
• $5=\sqrt{(0-x)^2+(0-y)^2}$

• $5=\sqrt{(-x)^2+(-y)^2}$
• $5=\sqrt{x^2+y^2}$
• Rewritting the equation we have
• $\sqrt{x^2+y^2}=5$
• Squaring on both the sides
• $(\sqrt{x^2+y^2})^2=5^2$
• $x^2+y^2=25$

Therefore  any points satisfying the equation $x^2+y^2=25$ is the coordinates of P