pancakes_fn
New member
- Joined
- Dec 6, 2019
- Messages
- 8
The curve 12x² - 5y² = 7 intersects the line 2p²x - 5y = 7 at the point (1,p).
(i) Find the value of p
(ii) Find the coordinates of the other point of intersection.
Here’s what I’ve got so far:
Equate both equations:
12x² - 5y² = 2p²x - 5y
Substitute (1,p):
12(1)² - 5(p)² = 2p²(1) - 5(p)
12 - 5p² = 2p² - 5p
12 - 5p² - 2p² + 5p = 0
-7p² + 5p + 12 = 0
7p² - 5p - 12 = 0
(7p - 12)(p + 1) = 0
p = 12/7 or p = -1
How do I continue?
How do I know which value is the correct one?
(i) Find the value of p
(ii) Find the coordinates of the other point of intersection.
Here’s what I’ve got so far:
Equate both equations:
12x² - 5y² = 2p²x - 5y
Substitute (1,p):
12(1)² - 5(p)² = 2p²(1) - 5(p)
12 - 5p² = 2p² - 5p
12 - 5p² - 2p² + 5p = 0
-7p² + 5p + 12 = 0
7p² - 5p - 12 = 0
(7p - 12)(p + 1) = 0
p = 12/7 or p = -1
How do I continue?
How do I know which value is the correct one?