LEARN · EXPLAIN · REVISE

Show there is one common point and explain why this line is not tangent.

Read the idea, work independently, then explain what changed.

TOPIC 01

Conic sections: mixed review

A mixed assessment: identify the method, justify it and revise your reasoning.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Transfer#Your turn

y=x+33, x^2-y^2=1089

a,b>0 and e>1; a distance difference is absolute, and an asymptote is not part of the curve.

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Translate the geometric condition into a coordinate equation.

Hint 2

Substitution cancels the quadratic terms.

Worked solution

Translate the geometric condition into a coordinate equation.
Apply the stated relation and retain its conditions.
$-66x-1089=1089 ⇒ x=-33, y=0$
Apply the stated relation and retain its conditions.
$\text{tangent at }P:x=-33$
The line is parallel to an asymptote; one intersection can result from degree reduction.

The requested relation or conclusion is shown below.

P=(-33,0)

Checks and common pitfalls: The line is parallel to an asymptote; one intersection can result from degree reduction.

Reasoning checklist · self / teacher assessment

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

Teacher preparation and assessment