Question

If AB is diameter of the circle x² + y² + 2x + 4y - 3 = 0. If co-ordinates of A are (1, 0), then co-ordinates of B are
1. (-3, 1)
2. (-3, 2)
3. (-3, 3)
4. (-3, -4)

Answer 1

Correct Answer - Option 4 : (-3, -4)

Concept:

f(x, y) = 0 → circle

Let center of the circle is (-f, -g) and

f(x, y) = x2 + y2 + 2fx + 2gy + c = 0 --- (1)

Calculation:

x2 + y2 + 2x + 4y - 3 = 0

Comparing with (1), we get

f = 1 & g = 2

center of circle (-1,-2)

Now, one end of diameter is (1,0)

mid point of diameter = center = (-1,-2)

Let the co-ordinate of other-end of the diameter = x₁, y₁

\(\frac{x_1 + 1}{2} = -1\)

x₁ + 1 = -2

x₁ = -3

\(\frac{y_1}{2}=-2\)

y₁ = - 4

The co-ordinates of other end of diameter are (-3, -4)