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

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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)

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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).

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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)

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

Last updated at March 16, 2023 by Teachoo

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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

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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