Question

please solve all question....

Answer 1

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Answer 2

Let the equation of the required circle be

(x – h)^2 + (y – k)^2 = r^2.

Since the centre of the circle passes through (0, 0),

(0 – h)^2 + (0 – k)^2 = r^2

⇒ h^2 + k^2 = r^2

The equation of the circle now becomes

(x – h)^2 + (y – k)^2 = h^2 + k^2.

It is given that the circle makes intercepts a and b on the coordinate axes. This means that the circle passes through points (a, 0) and (0, b).

Therefore,

(a – h)^2 + (0 – k)^2 = h^2 + k^2 …………………… (1)

(0 – h)^2 + (b – k)^2 = h^2 + k^2 …………………… (2)

From equation (1),

we obtain a^2 – 2ah + h^2 + k^2 = h^2 + k^2

⇒ a2 – 2ah = 0

⇒ a(a – 2h) = 0

⇒ a = 0 or (a – 2h) = 0

However, a ≠ 0; hence, (a – 2h) = 0 ⇒ h =a/2.

From equation (2)

, we obtain h2 + b2 – 2bk + k^2 = h^2 + k^2

⇒ b2 – 2bk = 0

⇒ b(b – 2k) = 0

⇒ b = 0 or(b – 2k) = 0

However,

b ≠ 0; hence, (b – 2k) = 0 ⇒ k =b/2.

Thus, the equation of the required circle is

x^2+y^2-ax-by=0