Ask Singapore Homework?
Upload a photo of a Singapore homework and someone will email you the solution for free.
Question
junior college 2 | H3 Maths
One Answer Below
Anyone can contribute an answer, even non-tutors.
Please help~~~~~~thank you
Date Posted: 5 years ago
Views: 1312
3y² - 2qy + 2y + q² - 2q - 3 = 0
3y² + y(2 - 2q) + q² - 2q - 3 = 0
Discriminant = b² - 4ac
= (2-2q)² - 4(3)(q² - 2q - 3)
= 4 - 8q + 4q² - 12q² + 24q + 36
= 16 q + 40 - 8q²
= 8 (2q + 5 - q²)
If q² < 2q + 5,
Then 2q + 5 > q²
2q + 5 - q² > 0
So 8(2q + 5 - q²) also > 0
So 16q + 40 - 8q² > 0
Thus, discriminant > 0
So the line will intersect the ellipse at two distinct(different) points.
3y² + y(2 - 2q) + q² - 2q - 3 = 0
Discriminant = b² - 4ac
= (2-2q)² - 4(3)(q² - 2q - 3)
= 4 - 8q + 4q² - 12q² + 24q + 36
= 16 q + 40 - 8q²
= 8 (2q + 5 - q²)
If q² < 2q + 5,
Then 2q + 5 > q²
2q + 5 - q² > 0
So 8(2q + 5 - q²) also > 0
So 16q + 40 - 8q² > 0
Thus, discriminant > 0
So the line will intersect the ellipse at two distinct(different) points.
See 1 Answer
360 Tutoring Program