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12 The straight line y = x + 1 intersects the curve x2 - y = 5 at the points A Given that A lies below the x-axis and the point P lies on AB such that AP: PB = 4:1, find the coordinates of P.​

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ferrybukantoro

Step-by-step explanation:

y= x+1 -> (y1)

x²-y = 5 => y = x²-5 -> (y2)

(y2) = (y1) =>

x²-5 = x+1

x²-x-6 = 0

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

x1=3 or x2 = -2

y1= 3+1 = 4

y2=-2+1 = -1

the intersects are : (3, 4) and (-2, -1)

so, the point A = (-2, -1) => lies below the x-axis.

and the point B = (3, 4)

the point P :

X = -2 + (4/5 × [3-(-2) ])

= -2 + (4/5 ×5)

= -2 +4 = 2

Y = -1 + (4/5 × [4-(-1) ])

= -1 +(4/5 ×5)

= -1 +4 = 3

so, the coordinates P = (2, 3)

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