Question

Tangents `P Qa n dP R` are drawn at the extremities of the chord of the ellipse `(x^2)/(16)+(y^2)/9=1` , which get bisected at point `P(1,1)dot` Then find the point of intersection of the tangents.

Answer 1

Correct Answer - `((144)/(25),(144)/(25))`

Eqution of chord having midpoint P(1,1) is
`(1*x)/(16)+(1*y)/(9)-1=(1)/(16)+(1)/(9)-1`
or `(x)/(16)+(y)/(9)=(25)/(144)`
`or 9x+16y=25" (1)`
Also, line QR is chord of contact w.r.t. point (h,k).
It equations is
`(hx)/(16)+(ky)/(9)=1`
or `9hx+16ky=144 " "(2)`
Equatiosn (1) and (2) represent the same stragith line.
`:. (9h)/(9)=(16k)/(16)=(144)/(25)`
`rArr(h,k)-=((144)/(25),(144)/(25))`