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Tangents are drawn to x^2+y^2=16 from th...

Tangents are drawn to `x^2+y^2=16` from the point `P(0, h)dot` These tangents meet the `x-a xi s` at `Aa n dB` . If the area of triangle `P A B` is minimum, then `h=12sqrt(2)` (b) `h=6sqrt(2)` `h=8sqrt(2)` (d) `h=4sqrt(2)`

A

h=`12sqrt(2)`

B

h=`6sqrt(2)`

C

h=`8sqrt(2)`

D

h=`4sqrt(2)`

Text Solution

Verified by Experts

The correct Answer is:
4

Let `angle COA =theta Then OA =OC sec theta =4 sec theta`
Also `angleOPC =theta .Then OP =OC cosec theta =4 cosec theta`
Now `triangle_(PAB)=OA OP =(32)/(sin 2 theta)`
For `triangle_(PAB)` to be minimum `sin 2 theta =1 or theta =(pi)/(4)`
`therefore P=0,4 sqrt(2)`
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