Question

If the point diametrically opposite to point $P(1,0)$ on the circle $x^2+y^2+2x+4y-3=0$ is $(a,b)$, then

• A. $|a|=3$
• B. $|b|=4$
• C. $|a|=4$
• D. $|b|=3$

Answer 1

Answer: (A), (B)

The correct options are
A $|a|=3$
B $|b|=4$

Given circle is $x^2+y^2+2x+4y-3=0$
Centre $=(-1,-2)$
Let $Q(a,b)$ be the point diametrically opposite to the point $P(1,0)$,
$\frac{1+a}{2}=-1,\frac{0+b}{2}=-2\Rightarrow a=-3,b=-4$