BITSAT 2022 Paper

Let P(t,4t−

20

5

) be a point on the line
4x−5y=20. Then the chord of contact of tangents drawn from P to the circle x2+y2=9 is
tx(4t−

20

5

)y=9...(i)
Let θ(h,k) be the mid-point of this chord of contact, then its equation is also hx+ky=h2+k2...(ii)
Clearly Eqs. (i) and (ii) represent the same line
∴

t

h

=

4t−20

5k

=

9

h2+k2

⇒

t

h

=

9

h2+k2

‌and‌

t

h

=

4t−20

5k

⇒t=9

h

h2+k2

‌and‌t=

20h

4h−5k

⇒9

h

h2+k2

=

20h

4h−5k

⇒h{20(h2+k2)−36h+45k}=0
x=0,or[20(x2+y2)−36x+45y]=0