Circle Test

Result

Circle Test - 2

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Weekly Quiz Competition

Question 1
1 / -0

If one circle of a co - axial system is x² + y² + 2gx + 2fy + c = 0 and one limiting point is (a, b) then equation of the radial axis will be

A
2gx + 2fy + c – a² – b² = 0

B
None of these

C
(g + a) x + (f + b) y + c – a² – b² = 0

D
2(g + a) x + 2(f + b) y + c – a² – b² = 0

Solution

Given circle S₁ = x² + y² + 2gx + 2fy + c = 0 ......(i)

∴ Equation of the second circle is

(x - a)² + (y - b)² = 0

S₂ = x² + y² - 2ax - 2by + a² + b² = 0 ......(ii)

From (i) and (ii), equation radical axis is S₁ - S₂ = 0

2(g + a)x + 2(f + b)y + c - a² - b² = 0
Question 2
1 / -0

The equation of the radical axis to the system of coaxial circles x² + y² + 2ax + 2by + c + 2λ (ax – by + 1) = 0 is

A
ax – by + 1 = 0

B
2(bx – ay) + 1 = 0

C
2(ax + by) + 1 = 0

D
bx + ay – 1 = 0

Solution

For any value of λ, the given equation represents circles passing through points of intersection of the circle

x² + y² + 2ax + 2by + c = 0 and the line ax - by + 1 = 0.

so, ax - by + 1 = 0 is the common chord for each circle of the system, hence it is the radical axis.