Question

the point (3,—4) the centre of a circle.If AB is a diameter of the circle and B is (5,—6) find the coordinates of A​

Answer 1

Explanation:

Given:-

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).

Answer 2

Answer:

If AB is a diameter of the circle and $B$ is $(5, -6)$ , the coordinates of $A$ were found to be  $(1, -2)$

Explanation:

$P (3, -4)$ center

$B(5, -6)$ and let $A$ be ($x_1 + y_1$)

Midpoint = $(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2 }{2})$

$A(x_1, y_{1}) B (5, -6)$

$(3, -4) = [\frac{x_{1}+ 5 }{2}, \frac{y_{1}+ (-6) }{2}]$

Let's take the co-ordinate of $3$,

$3 = (\frac{x_{1}+ 5 }{2})$

$3$ × $2 = x_{1} + 5$

$6 - 5 = x_{1}$

$1 = x_{1}$

Therefore $x_{1} = 1$

Let's take the co-ordinate of $-4$,

     $-4 = \frac{y_{1} - 6 }{2}$

$-4$ × $2 = y_{1} - 6$

$-8 + 6 = y_{1}$

$-2 = y_{1}$

Therefore, $y_{1} = -2$

Therefore, the coordinates of A is $(1, -2)$

To know more about the center, visit:

https://brainly.in/question/15017963

To know more about diameter, visit:

https://brainly.in/question/1737906

#SPJ2