Question

A line having slope '1' is drawn fram a point A(-3, 0) cuts a curve y=x^2+x+1 at P & Q. Find l(AP) l(AQ).

Answer 1

the line equation : y = ax + b

point A ( -3 , 0) satisfies the line eq .

0 = -3 * a + b

slope = 1 =  a

b = 3

the line eq. y =  a + 3

the line cuts the curve at p & Q\

so , x +3 = x² +x +1

x² = 2

x = √2  , -√2

P ( √2 , 3+√2  )

Q ( -√2 , 3-√2)

then you can find the distance by s.r

L AP = √((XA - XP )² + ( YA - YP)²)

same for L AQ