Question

A line having slope 1 is drawn from a point A (-3,0) cuts a curve y=x​​​​​x^{​​​​​2}+x+1 at P and Q . Find l(AP) and 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