Formula for Circle:
(X - a)^2 + (Y - b)^2 = (r)^2
Where point (a , b) is the Center of the Circle and r is the Radius
Since we are given the 2 points as the Diameter of the Circle, the Diameter = D = 6 units along X axis from point A to point D
The Radius = r = 3
The Center will be the mid point of the Diameter on the X Axis, which occurs at point (2 , 0)
The formula of the Circle is given by:
(X - 2)^2 + (Y)^2 = 9
Now, since we are told that point C is on the circumference of the circle, we have an inscribed 90 degree triangle with the hypotenuse as the diameter.
Using the Hypotenuse as the Base of the triangle, we can find the Height of this Triangle that extends from the Base (Diameter/Hypotenuse) to the 90 degree vertex at C
Area of triangle = (1/2) * (6) * (h) = (6) * sqrt(2)
Perpendicular Height from Diameter/Hypotenuse to the vertex at Point C = h = 2 * sqr(2)
Given that the Base we used is on the X Axis, this perpendicular height - h - will be given by the Y Coordinate of Point C.
In other words, the height will be equal to the distance as measured by the Y Axis from Y = 0 to vertex C ——> which is given by the Y coordinate of point C
Thus, the Y coordinate of point C must either be:
2 * sqrt(2)
or
(-)2 * sqrt(2)
We can eliminate 3 options, leaving only A and B.
If you are short on time, you can visualize the circle on the graph paper and realize that the Point given by (0 , 2*sqrt(2) )
Will be Outside the edge of the Circle.
To confirm that answer B lies on the circle, you can plug the coordinates into the equation for the circle that we have.
When you plug the coordinates given in answer B into:
(X - 2)^2 + (Y)^2 = 9
You will find that the equation is satisfied and that vertex C lies on the circumference of the circle.
Answer (B)
DrMudassir wrote:
kapil, A is lying on the y axis.
I still don't understand why eliminate A
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