Write the equation of each circle Center (-1,0) and containing the point (2, -4)

A.(x + 1)2 + y2 = 25
B.x2 + (y2 +1)= 25

The equation of the circle is

Step-by-step explanation:

Equation of a circle:

The equation of a circle of centre has the following format:

In which r is the radius.

Center (-1,0)

This means that . So

Finding the radius:

Distance between the radius and the centre and a point of the circle. In this case, point (2,-4). Using the formula for the distance between two points:

So, the equation of the circle is:

The correct option for the missing statement of Step 7 of the two column proof is option D.

D. Consecutive ∠s in a parallelogram are supplementary

The reason for the above selection is presented as follows;

The given two column proof is presented as follows;

Statement                                Reason

1. WXYZ is a parallelogram; ZX ≅ WY       1. Given

2. ZY ≅ WX                                 2. Opp. sides of parallelogram are ≅

3. YX ≅ YX                                  3. Reflexive property

4. ΔZYX ≅ ΔWXY                        4. SSS ≅ thm.

5. ∠ZYX ≅ ∠WXY                      5. CPCTC

6. m∠ZYX ≅ m∠WXY                 6. Def. of ≅

7. m∠ZYX + m∠WXY = 180°      7. Consecutive ∠s in a parallelogram are supplementary

8. m∠ZYX + m∠ZYX = 180°       8. Supplementary property

9. 2(m∠ZYX) = 180°                    9. Simplification

10. m∠ZYX = 90°                        10. Division Property of equality

11. WXYZ is a rectangle             11. Rectangle ∠ theorem

Where;

Def = Definition

Opp. = Opposite

≅ = Congruent

CPCTC = Congruent Parts of Congruent Triangles are Congruent

The missing reason is that in a parallelogram, consecutive angles are supplementary

Learn more about parallelograms here:

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