Unit 3 lesson 9 recap circle equations

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• Wiskunde
• Middelbare school
• vwo
• Leerjaar 4

Welcome MYP5!

Today

• one more example on the distance between points and lines

• continue with circle equations

example together

Distance between a point and line formule

Point A

Line l

Lets do question b with this formule

Slide tekst

First we need the line m formule:

Slope: ? what is a?

y=ax+b

Leerdoelen today

You know the general form of a circle equation

You can compose the equation for a circle

What if there is a point M, and we are looking for all the points that have a certain distance r to M. How would we find all these points?

(x − x_M)² + (y − y_M)² = r²

what is the formula for the circle in the figure?

https://www.geogebra.org/m/U2CwyvrU

If line k is tangent to circle c with centre M and radius r at point A, then MA ⊥ k and d(M, k) = r.

Example 1/2

There are two circles c₁ and c₂ whose centre lies on the line , which have radius 3 ("straal") and are tangent to ("raken") the x-axis. Find an equation for both c₁ and c₂.

$$k:y=\frac{1}{2}x-2$$

Example 2/2 (together)

Homework

Worksheet 3.5: circle equations