Answer:
<h3>#1</h3>
The normal overlaps with the diameter, so it passes through the center.
<u>Let's find the center of the circle:</u>
- x² + y² + 2gx + 2fy + c = 0
- (x + g)² + (y + f)² = c + g² + f²
<u>The center is:</u>
<u>Since the line passes through (-g, -f) the equation of the line becomes:</u>
- p(-g) + p(-f) + r = 0
- r = p(g + f)
This is the required condition
<h3>#2</h3>
Rewrite equations and find centers and radius of both circles.
<u>Circle 1</u>
- x² + y² + 2ax + c² = 0
- (x + a)² + y² = a² - c²
- The center is (-a, 0) and radius is √(a² - c²)
<u>Circle 2</u>
- x² + y² + 2by + c² = 0
- x² + (y + b)² = b² - c²
- The center is (0, -b) and radius is √(b² - c²)
<u>The distance between two centers is same as sum of the radius of them:</u>
<u>Sum of radiuses:</u>
<u>Since they are same we have:</u>
- √(a² + b²) = √(a² - c²) + √(b² - c²)
<u>Square both sides:</u>
- a² + b² = a² - c² + b² - c² + 2√(a² - c²)(b² - c²)
- 2c² = 2√(a² - c²)(b² - c²)
<u>Square both sides:</u>
- c⁴ = (a² - c²)(b² - c²)
- c⁴ = a²b² - a²c² - b²c² + c⁴
- a²c² + b²c² = a²b²
<u>Divide both sides by a²b²c²:</u>
Proved
Applying the distance formula, the lengths of the segments are:
WX= √26 = 5.1 units
YZ = √26 = 5.1 units
XY = √26 = 5.1 units
WZ = √26 = 5.1 units
WY = √26 = 5.1 units
XZ = √52 = 7.2 units
<h3>The Distance Formula</h3>
The distance formula, , can be used to find the distance between two endpoints of a segment.
Given:
- W(-4, -3)
- X(1, -2)
- Y(2, -7)
- Z(-3, -8)
Find WX:
Let:
W(-4, -3) = (x1, y1)
X(1, -2) = (x2, y2)
Plug in the values into the distance formula:
Following the same steps, using the distance formula, the following lengths would be calculated as follows:
YZ = √26 = 5.1 units
XY = √26 = 5.1 units
WZ = √26 = 5.1 units
WY = √26 = 5.1 units
XZ = √52 = 7.2 units
Learn more about distance formula on:
brainly.com/question/1872885
Answer:
B
Step-by-step explanation:
the reason is the
Answer:
54 cm²
Step-by-step explanation:
Area of Parrelogram= Length×Breadth
You see, if u move the triangles to he other side, you'll get a rectangle. So you can just take the length multiply by the breadth.
Area=9×6=54 cm²
I did not use meters to find the area. I did not use it as the questions already shows the measurement as centimeters, so if I use meters, I will have to convert it to centimeters.