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# find the coordinates of point a where ab is the diameter of the circle

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### Mohammed

Guys, does anyone know the answer?

get find the coordinates of point a where ab is the diameter of the circle from screen.

## Find the coordinate of a point A, where AB is the diameter of a circle whose centre is (2,

Click here👆to get an answer to your question ✍️ Find the coordinate of a point A, where AB is the diameter of a circle whose centre is (2, - 3) and B is (1,4)

Question

## Find the coordinate of a point A, where AB is the diameter of a circle whose centre is (2,-3) and B is (1,4)

Given:-

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A circle with centre (2,−3) and AB is the diameter of circle with B(1,4).

To find:- Coordinate of point A.

Let (x,y) be the coordinate of A.

Since AB is the diameter of the circle, the centre will be the mid-point of AB.

now, as centre is the mid-point of AB.

x-coordinate of centre =

2 x+1 ​

y-coordinate of centre =

2 y+4 ​

But given that centre of circle is (2,−3).

Therefore, 2 x+1 ​ =2⇒x=3 2 y+4 ​ =−3⇒y=−10

Thus the coordinate of A is (3,−10).

Hence the correct answer is (3,−10).

1382 162

स्रोत : www.toppr.com

## Find the coordinates of a point A, where AB is a diameter of a circle with centre (

Q.1 of chapter 1, All India - 2019 - Mathematics - Board Papers book. Find the coordinates of a point A, where AB is a diameter of a circle with centre (-2,2) and B is the point (3, 4).

1

Find the coordinates of a point A, where AB is a diameter of a circle with centre (-2,2) and B is the point (3, 4).

Let O be the centre of AB.

Since AB is the diameter, so O is the midpoint of AB.

By section formula which states that if a point P (x , y) divides the line with end points A(x1,y1) and B(x2,y2) in the ration m:n, the coordinates of x and y are:

As midpoint divides the line in the ratio 1:1,

Then, the coordinates of A (x, y) can be calculated as:

⇒ a + 3 = 2(-2) ⇒ a + 3 = -4 ⇒ a = -7 And, ⇒ b + 4 = 2(2) ⇒ b + 4 = 4 ⇒ b = 0

Hence, coordinate of point A is (-7,0).

स्रोत : philoid.com

## Ex 7.2, 7

Ex 7.2, 7 Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, – 3) and B is (1, 4). Let the circle be as shown with centre C (2, −3) Let AB be the diameter of the circle Since AB is the diameter, Centre C must be the mid−point of AB Let A(x, y)

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## Ex 7.2, 7 - Chapter 7 Class 10 Coordinate Geometry (Term 1)

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### Transcript

Ex 7.2, 7 Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, – 3) and B is (1, 4). Let the circle be as shown with centre C (2, −3) Let AB be the diameter of the circle Since AB is the diameter, Centre C must be the mid−point of AB Let A(x, y) Since C is the mid−point of AB x−coordinate of C = (𝑥1 + 𝑥2)/2 y−coordinate of C = (𝑦1 + 𝑦2)/2 Where x1 = x, y1 = y x2 = 1, y2 = 4 Hence the coordinates of A(x , y) = A(3, −10) x−coordinate of C = (𝑥 + 1)/2 2 = (𝑥 + 1)/2 2 × 2 = x + 1 4 = x + 1 4 – 1 = x 3 = x x = 3 y−coordinate of C = (𝑦 + 4)/2 −3 = (𝑦 +4)/2 −3 × 2 = y + 4 −6 = y + 4 −6 – 4 = y −10 = y y = −10

Next: Ex 7.2, 8 →