Based on the given figure, the table should be completed to derive the equation of a circle in standard form as follows:
Statements Reasons______________
DE = y - k From figure.
EC = x - h From figure
DC² = DE² + EC² Pythagorean theorem
(x - h)² + (y - k)² = r² Pythagorean theorem
What is a circle?
A circle can be defined as a closed, two-dimensional curved geometric shape with no edges or corners. Also, a circle refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point (central axis).
The equation of a circle.
Mathematically, the standard form of the equation of a circle is given by;
(x - h)² + (y - k)² = r²
Where:
- h and k represents the coordinates at the center.
- r represents the radius of a circle.
Statements Reasons______________
1. DJ ⊥ x-axis By construction
2. CE ⊥ DJ By construction__________
3. DJ = y From figure
4. EJ = k From figure
5. DE = DJ - EJ From figure
6. DE = y - k From figure_____________
7. EL ⊥ y-axis By construction__________
8. EL = x From figure
9. CL = h From figure
10. EC = EL - CL From figure
11. EC = x - h From figure_____________
12. ΔDEC is a right triangle m∠DEC = 90°
13. DC² = DE² + EC² Pythagorean theorem
14. (x - h)² + (y - k)² = r² Pythagorean theorem
Read more on circle coordinates here: brainly.com/question/1615837
#SPJ1
