Question

find the role of the line 2x+3y_4=0 with respect to the parabola y^2=4x​

Answer 1

Answer:

given line cuts the parabola in two different points.

it passes through it.

Step-by-step explanation:

given:

parabola is y²=4x ------1

line is 2x+3y-4 = 0 -----2

2x = 4-3y

4x = 8-6y

substitute this in parabola,

y² = 8-6y

y²+6y-8 =0

now, determine whether the above equation has real roots by b²-4ac,

= 6²- 4*1*(-8)

= 36+32

= 68

as b²-4ac >0, it has two real distinct roots,

that means given line cuts the parabola in two different points.