Question

Please give correct answer​

Answer 1

Question: A circle is drawn on the chord of a circle x^2 + y^2 = a^2 as diameter. The chord lies on the line x + y = a. What is equation of the circle.

Answer:

Let the points where end points of diameter of smaller circle touch the bigger circle be (h, k).

For (x, y) = (h, k) :

h² + k² = a² and h + k = a → k = a - h

=> h² + (a - h)² = a²

=> 2h² - 2ah = 0

=> h = 0 or a

thus, k = a - 0 = a or a - a = 0

Hence, the points are (0, a) and (a, 0).

Using distance formula,

Diameter = √(0 - a)² + (a - 0)² = a√2

Radius = (a√2)/2

Centre of smaller circle = mid point of diameter

Using mid point formula,

Centre = (a+0/2, 0+a/2) = (a/2 , a/2)

Therefore, required equation is

=> (x - a/2)² + (y - a/2)² = (a√2/2)²

=> 4x² + 4y² + 2a² - 4ax - 4ay = 2a²

=> x² + y² - ax - ay = 0

Answer 2

Answer:

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