Question

Equation of a straight line meeting the circle $x^2+y^2=100$ in two points each point at a distance of $4$ from the point $(8,6)$ on the circle is

• A. $4x+3y-50=0$
• B. $4x+3y-100=0$
• C. $4x+3y-46=0$
• D. none of these

Answer 1

The correct option is A $4x+3y-50=0$

Given circle $S:x^2+y^2=100$

Let $P,Q$ be the two points meeting the circle, $A$ be the point (8,6)

Given $PA=QA=4$

$⟹PA$and $QA$ are tangents and $PQ$ is the COC corresponding to A.

Equation of COC is given by $T=0$

Where $T$ is $x{x}_1+y{y}_1+a^2$ for a circle $x^2+y^2=a^2$ and a point $(x_1,y_1)$ lying outside.

$⟹8x+6y=100$ is the equation of PQ.

$4x+3y–50=0$