Question

Tangents are drawn from $P(3,0)$ to the circle $x^2+y^2=1$ touches the circle at points $A$ and $B$. The equation of locus of the point whose distances from the point $P$ and the line $AB$ are equal is

• A. $9y^2+48x-80=0$
• B. $9y^2-48x+80=0$
• C. $3y^2-12x+39=0$
• D. $3x^2-12x+39=0$

Answer 1

The correct option is B $9y^2-48x+80=0$

$S:x^2+y^2=1$

The equation of chord of contact $AB$ is $S_1=0⟹x=\frac{1}{3}$

Let $(h,k)$ be a point on the locus

From the given conditions

$\sqrt{(h-3{)}^2+k^2}=(h-\frac{1}{3})$

$(h-3{)}^2+k^2=(h-\frac{1}{3}{)}^2⟹9k^2-48h+80=0$

The locus is $9y^2-48x+80=0$