LEARN · EXPLAIN · REVISE

Find the tangent of slope 1 to y²=4tx.

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 / Standard#Your turn

t=28

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Translate the geometric condition into a coordinate equation.

Hint 2

Use this intermediate relation.

y=x+b\Rightarrow x^2+(2b-4t)x+b^2=0

Worked solution

Translate the geometric condition into a coordinate equation.
Apply the stated relation and retain its conditions.
$\Delta=(2b-112)^2-4b^2=448(28-b)$
Apply the stated relation and retain its conditions.
$\Delta=0\Rightarrow b=28$
The quadratic coefficient remains nonzero, so a repeated root establishes tangency.

The requested relation or conclusion is shown below.

y=x+28

Checks and common pitfalls: The quadratic coefficient remains nonzero, so a repeated root establishes tangency.

Reasoning checklist · self / teacher assessment

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

Teacher preparation and assessment