Question

QUESTION#1; Consider the equation of a circle If the line is its diameter. Then find the value of a.

ANSWER; Solution

Given Data

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Consider the equation of the circle.











From this equation we can understand that the center of the circle is (1, 2) and the radius is 3 units.

[Recall that the general equation of a circle of radius r with center at (h, k) is (x - h)² + (y - k)² = 1.]

Since the line 2x - y + a = 0 is a diameter of the circle, (1, 2) is a point on the line as diameter passes through the center.

So taking (x, y) = (1, 2),





Hence the value of a is 0.

OR

We proof that a value is 0

​

Answer 1

So what's the actual question here?

Answer 2

The value of a is 0.

Given,

The equation of diameter of the circle is 2x-y+a = 0.

The center of the circle is (1,2).

To Find,

The value of a.

Solution,

Diameter of the circle is the longest chord of the circle passing through the center of he circle.

So, the coordinates of the center of the circle will satisfy the equation of diameter of the circle.

Now, substituting the values in the equation

2x-y+a = 0

2(1)-y(2)+a = 0

2-2+a = 0

a = 0

Hence, the value of a is 0.

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