Question

if the point (x,4) lies on the circle whose centre is at the origin and radius is 5 ,then find the value of x

Answer 1

Answer:

x= + Or - 3

Step-by-step explanation:

(x, y) (0,0)

root over √(0-x)²+(0-4)²=5

root over√0²+x²+16=5

squaring on both sides:

(√x²+16)²=5²

square and root get cancelled

x²+16=25

x²=25-16

x²=9

x=√9

x=+ Or - 3

Answer 2

Given: The point (x,4) lies on the circle whose centre is at the origin and radius is 5.

To find: Value of x

Solution: The equation of a circle is given by:

${(x - a)}^{2} + {(y - b)}^{2} = {r}^{2}$

where (a,b) is ghe in centre of the circle and r is the radius of the circle.

r = 5

Here, origin is the centre of the circle. Therefore:

(a,b) = (0,0)

Therefore, equation of the circle:

${(x - 0)}^{2} + {(y - 0)}^{2} = {(5)}^{2}$

$= > {x}^{2} + {y}^{2} = 25$

Since (x,4) lies on the circle, this point should satisfy the equation of the circle. Therefore,

${x}^{2} + {(4)}^{2} = 25$

$= > {x}^{2} + 16 = 25$

$= > {x}^{2} = 25 - 16$

$= > {x}^{2} = 9$

$= > x = \sqrt{9}$

=> x = 3 or x = -3

Therefore, the value of x is equal to 3 or -3.