<span>x² +y² -4x -6y +8=0
(x² -4x) +(y² -6y) = -8
We are going to complete square for x and y,
it should look like a²+2ab+b² = (a +b)², or </span>a²-2ab+b² = (a -b)²,
<span>
(x²-2*2x+2²) -2² + (y²-2*3y +3²)-3²=- 8
(x-2)²+(y-3)²-4-9=-8
</span>(x-2)²+(y-3)²=-8+13
(x-2)²+(y-3)²=5
<span>
Formula a circle (x-h)²+(y-k)²=R², where vertex has coordinates (h, k)
So , for our circle vertex (2,3) and radius = </span>√5<span>
</span>
Answer:

Step-by-step explanation:
<em>Given:</em>
Mn is diameter of circle having centre O
and BD = OD,
<em><u>To prove that:</u></em>
<u>
</u>
<em>Solution:</em>
Join the points O and B and draw OB,
On joining the line,
in ∆OCD and ∆OBD,
OC =OB → (Radius of same circle)
BD =CD → (from given)
OD =OD → (Common side in both the triangles)
Hence ∆OCD and ∆OBD are congruent from SSS property.
so we can say that,

Consider above prove as statement A
Corresponding angles of congruent traingle.
in ∆ OAB,
OA = OB (radius of same circle)
hence ∆OAB is an isosceles traingle.
We know that opposite angle of isosceles traingle are always equal. hence,

Consider above prove as statement B
From Statement A & B we can say that

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Answer:
4m3+18m2−34m+12
Step-by-step explanation:
=(4m+−2)(m2+5m+−6)
=(4m)(m2)+(4m)(5m)+(4m)(−6)+(−2)(m2)+(−2)(5m)+(−2)(−6)
=4m3+20m2−24m−2m2−10m+12
Step-by-step explanation:
The area of a rectangle is 171 m²
Let l is the length and b is the width of the rectangle
It width is 10 m less than the length. So,
b = l-10 ...(1)
Area of a rectangle is given by :

or
l = 9 m or l = 19 m
If l = 9 m,
b = 9-10 = -1 m (can't be possible)
If l = 19 m
b = 19-10 = 9 m
So, the length an the breadth of the rectangle is 19 m and 9 m respectively.