Question

Recall the equation for a circle with center ( h , k ) and radius r . At what point in the first quadrant does the line with equation y = 2.5 x + 4 intersect the circle with radius 5 and center (0, 4)?

Answer 1

Answer: The required point = (1.857,8.643)

Explanation:

Equation of circle with center (h,k) and radius r:
`(x-h)^2+(y-k)^2=r^2`

Given: Radius = 5 , center = (0,4)

Eqation of circle:
`(x-0)^2+(y-4)^2=5^2`

`x^2+(y-4)^2=25`

`x^2+(2.5x+4-4)^2=25` [Using equation y = 2.5 x + 4 ]

`x^2+(2.5x)^2=25`

`x^2+6.25x^2=25`

`7.25x^2=25`

`x^2=3.44827586207`

`x=1.857`

`y= 2.5(1.857)+4`

`=8.6425`

Hence, the required point = (1.857,8.643)