Show the equation satisfied by the abscissae of the two intersections.

01 / Standard#Your turn

H:x^2-\frac{y^2}{4}=1,\quad L:y=m(x-\sqrt5)

Official paper · jm02-2024 · 3(a) · PDF 5

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Substitute y from the line into the hyperbola.

Hint 2

Expand (x−√5)² and collect terms.

Worked solution

(m²−4)x²−2√5m²x+5m²+4=0.

Checks and common pitfalls: Keep the cross term −2√5x in the square.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Clear the denominator after substitution.
$4x^2-m^2(x-\sqrt5)^2=4$
Collect and reverse the signs.
$(m^2-4)x^2-2\sqrt5m^2x+5m^2+4=0$

Think first. Reveal a hint when the class is ready.

2024 JM02