Question

A line through (2, 1) meets the curve x²-2x-y=3 at A(-2,5) and at B. FIND THE COORDINATES OF B

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Answer 1

(3,0)

Explanation:

We know the line will Pss through

(-2,5) and (2,1) so

let find the slope

`(1 - 5)/(2 - ( - 2)) = ( - 4)/(4) = - 1`

So the slope is -1.

We know it passes through 2,1 so use point slope to find b.

`y - 1 = - 1(x - 2)`

`y - 1 = - x + 2`

`y = - x + 3`

Set that equal to

`{x}^(2) - 2x - y = 3`

`{x}^(2) - 2x - 3 = y`

`{x}^(2) - 2x - 3 = - x + 3`

`{x}^(2) - x - 6 = 0`

`(x - 3)(x + 2) = 0`

`x = 3`

Point (3,0).