Question

Find the equation of chord centered at the point (1, 2) in the circle $x^2+y^2=9.$

• A. x + 2y - 5 = 0
• B. x - 2y - 5 = 0
• C. x - 2y + 5 = 0
• D. x + 2y + 5 = 0

Answer 1

The correct option is A

x + 2y - 5 = 0

If we have the slope of the line, we can write the equation of the chord. For that we can use the fact that the chord is perpendicular to the radius passing through the given point (1, 2). i.e., the products of the slopes will be (-1).

Given circle is

$\therefore$ Slope of OP=$\frac{2-0}{1-0}=2$

$\therefore$ Slope of AB=$\frac{(-1)}{2}$

$=\frac{-1}{2}$

$\therefore$ Required equation of chord is

$y-2=\left(\frac{-1}{2}\right)(x-1)$

$2y-4=-x+1$

$x+2y-5=0$