Question

find the coordinates of a point A, where AB is the diameter of a circle whose center is ( -2,3) and B is ( 1,4)​

Answer 1

Given :-

• Centre coordinates = (-2,3)
• B coordinates = (1,4)

To Find :-

• coordinates of Point A ?

Formula used :-

• Mid - Point formula Says That, The coordinates of two points (x1,y1) & (x2,y2) is given by (x1 + x2)/2 & (y1+y2)/2
• Length of Radius from Centre to circle is same.

Solution :-

Distance b/w centre to B = Distance b/w centre to A (Radius).

Let Coordinates of A are (x ,y) .

So, we can say That, Centre is Mid - Point of AB.

So,

→ (-2) = [ (x + 1)/2 ]

→ (-4) = x + 1

→ x = (-4) - 1

→ x = (-5)

and,

→ 3 = [ (y + 4)/2 ]

→ 6 = y + 4

→ y = 6 - 4

→ y = 2 .

Hence, The Coordinates of A are (-5 , 2).

Answer 2

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$\huge\tt{QUESTION:}$

find the coordinates of a point A, where AB is the diameter of a circle whose center is ( -2,3) and B is ( 1,4)

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$\huge\tt{GIVEN:}$

• Center coordinates =(-2,3)
• B coordinates = (1,4)

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$\huge\tt{TO~FIND:}$

• Cordinates of point A

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$\huge\tt{FORMULA~USED:}$

• Mid-point formulas

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$\huge\tt{SOLUTION:}$

↪Distance between center to B = Distance between center to A or Radius

Let cordinates of A be (x,y)

Then,

We can say the centers are mid-points of AB

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So for x,

↪(-2) =[(x+1)/2]

↪(-4)= x+1

↪x = (-4) -1

↪x = -5

and for y,

↪3 = [(y+4)/2]

↪6= y+4

↪y = 6-4

↪y = 2

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