LEARN · EXPLAIN · REVISE

Find the number of common points.

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

TOPIC 01

Equations of lines and circles: 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 / Foundation#Your turn

x^2+y^2=576,\quad y=24

Compare center distance with r1+r2 and |r1−r2|; equal centers require separate treatment.

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.

d=r

Worked solution

Translate the geometric condition into a coordinate equation.
Apply the stated relation and retain its conditions.
$d=24=r\Rightarrow\text{tangent}$
Equality gives one tangent point.

The requested value is 1.

Checks and common pitfalls: Equality gives one tangent point.

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

Teacher preparation and assessment