Question

A curve y=3 sqrt x and the line y=x interesct at O and P. Find the coordinates of P

Answer 1

It's simultaneous equation right? But, how do I solve it?

x= 3 sqrt x

Answer 2

right,
sqrt x=3
so, x=9
y=x=9
so, co-ordinates of P=(9,9)

Answer 3

x^2 = 9x
x^2-9x = 0
x(x-9) = 0
x = 0
x = 9

did i do it right? haha

Answer 4

9,9 assuming O is origin.

Answer 5

lol

Answer 6

Wait, there are different answers.... How do I do this?

Answer 7

or 0,0 assuming that O is not origin...it's not really specified which of O and P is origin

Answer 8

x^2=9 right?
so isn't that x=3 or x=-3?

Answer 9

O is the origin

Answer 10

x^2=9x

Answer 11

x = 3 sqrt x

square that.. x^2 = 3^2 (sqrt x)^2 so you still have an x

Answer 12

So, what's the answer? -3 and 3, or what?

Answer 13

either (0,0) or (9,-9)

Answer 14

(9.9) i mean

Answer 15

Are you sure?

Answer 16

considering 3 of us answered that..i am assuming we are sure

Answer 17

\[y=3\sqrt{x}\]Put y=x into the equation \[x=3\sqrt{x}\]Square both sides\[x^2=(3\sqrt{x})^2\]\[x^2=9x\]\[x^2-9x=0\]\[x(x-9)=0\]x=0 or x-9 =0
x=0 or x=9
therefore (0,0) and (9,9) are the intercepts (since y=x)

Answer 18

As O is the origin, that is (0,0), P is (9,9)

Answer 19

Thanks, that cleared it up :)