Distance formula

Question

Find the y coordinates of the points that are 10 units away from the point (-7,6) that have an x- coordinate of 1?

Answer 1

No this is NOT the distance formula.

All of the points that are 10 units from (-7,6) fall on the circle the equation of which is

(x+7)² + (y-6)² = 100

Substituting x=1 gives 8² + (y-6)² = 100

64 + y² - 12y + 36 = 0

y² - 12y = 0 and the co-ordinates are (1,12) and (1,0)

Answer 2

Distance formula: d² = (x₂ - x₁)² + (y₂ - y₁)².

Distance, d, = 10

Point 1 = (x₁,y₁) = (-7,6)

Point 2 = (x₂,y₂) = (1,y₂)

10² = (1-(-7))² + (y₂-6)²

100 = (1+7)² + y₂² - 12y₂ + 36

100 = (8)² + y₂² - 12y₂ + 36

100 = 64 + y₂² - 12y₂ + 36

100 = 100 +y₂² -12y₂

0 = y₂(y₂ - 12)

y₂ = 0, 12

So, the 2 points that are 10 units from the given point and have 1 as the x coordinate are (1,0) and (1,12).