Question

The equation of the circle with centre at (1, –2) and passing through the centre of the given circle $x ^ { 2 } + y ^ { 2 } + 2 y - 3 = 0$, is.

• A. $x ^ { 2 } + y ^ { 2 } - 2 x + 4 y + 3 = 0$
• B. $x ^ { 2 } + y ^ { 2 } - 2 x + 4 y - 3 = 0$
• C. $x ^ { 2 } + y ^ { 2 } + 2 x - 4 y - 3 = 0$
• D. $x ^ { 2 } + y ^ { 2 } + 2 x - 4 y + 3 = 0$

Answer 1

Answer: (A)

$x ^ { 2 } + y ^ { 2 } - 2 x + 4 y + 3 = 0$

Answer 2

According to the question, the required circle passes through (0,–1). Therefore, the radius is the distance between the points (0, –1) and (1, –2) i.e., $\sqrt { 2 }$ .

Hence the equation is $( x - 1 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = ( \sqrt { 2 } ) ^ { 2 }$

$\Rightarrow x ^ { 2 } + y ^ { 2 } - 2 x + 4 y + 3 = 0$

Trick : Since this is the only circle passing through

(0, –1).