Question

Find the length of the chord of contact of the tangents drawn from the point (3, 2) to the hyperbola $x^2-9y^2=9$.

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Equation of the chord of contact of the tangents drawn from the point (3, 2) to the hyperbola

T=0

$3x-9\times 2y=9$

x-6y=3 .........(1)

inter-section point of chord of contact x-6y=3 & hyperpola $x^2-9y^2=9$ is

$(3+6y{)}^2-9y^2=9$

$(1+2y{)}^2-y^2=1$

$1+4y^2+4y-y^2=1$

y(3y+4)=0

$y=0$ & $y=-\frac{4}{3}$

When y=0,x=3

when $y=-\frac{4}{3},x=6\left(\frac{-4}{3}\right)+3=-5$

point of intersection of chord of contact & hyperpola is

(3,0) & $(-5,-\frac{4}{3})$

Length of the chord of contact=$\sqrt{{(\frac{-4}{3}-0)}^2+(-5-3{)}^2}$

=$\sqrt{\frac{16}{9}+64}$

=$\sqrt{\frac{16+576}{9}}$