Question

The number of integral values of y for which the chord of the circle $x^2+y^2=125$ passing through the point $P(8,y)$ gets bisected at the point $P(8,y)$ and has integral slope is

• A. $8$
• B. $6$
• C. $4$
• D. $2$

Answer 1

The correct option is B $6$

Equation of chord to the given circle at point $P(8,y)$ as mid point is given by,
$T=S_1\Rightarrow 8x+y.y=125$
Now slope of this curve is, $m=-\frac{8}{y}$
Now for integral slope, integral values of $y$ possible is, $-1,-2,-4,4,2,1$
Hence total 6 integral values of $y$ are possible for the required condition.