Question

Find the range of values P such that the straight line y=px +1 does not intersect the parabola y²=8x

Answer 1

aw c'mon I've bumped twice

Answer 2

I have found a graphical approach... do you have use of a graphing calculator?

Answer 3

I need to do it mathematically

Answer 4

do you know how we find the intersection points ?

Answer 5

no ?

Answer 6

you will need to equate the 2 curves equal to each other,
by squaring both sides of y= px +1
so if you equate them, you will get a quadratic in 'x'

Answer 7

the roots of that quadratic equation are the points of intersection of those 2 curves.

Answer 8

sin we need them to NOT intersect, we will conclude that the quadratic equation has IMAGINARY roots.

Answer 9

and equate the discriminant part b^2-4ac as negative
b^2-4ac < 0
that will give you range of p

Answer 10

@StudyMathlol follow Hartnn's explanation they are pretty sound!

Answer 11

@hartnn can we find the values of P for which both of them intersect and subtract from R?

Answer 12

try it out.
if you get the same answer as that we get by my method, then YES,
else no.

Answer 13

does it sound about right anyway?

Answer 14

yes, but why you want to do 2 steps when it can be done in 1.

Answer 15

y=px+1
y^2=8x
(px+1)^2=8x
\[p^2 x^2+ 1 +2px=8x\]
how can we solve this? :P

Answer 16

you don't solve the equation
you find, a,b,c and then
b^2-4c <0

Answer 17

okay got it :D

Answer 18

@StudyMathlol
did you get what i am trying to explain ?