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Question Number 57289 by rahul 19 last updated on 01/Apr/19

Tangents are drawn to x^2 +y^2 =16 from  the point P(0,h).These tangents meet  the x−axis at A and B. If area of ΔPAB  is minimum then find value of h ?

$${Tangents}\:{are}\:{drawn}\:{to}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{16}\:{from} \\ $$$${the}\:{point}\:{P}\left(\mathrm{0},{h}\right).{These}\:{tangents}\:{meet} \\ $$$${the}\:{x}−{axis}\:{at}\:{A}\:{and}\:{B}.\:{If}\:{area}\:{of}\:\Delta{PAB} \\ $$$${is}\:{minimum}\:{then}\:{find}\:{value}\:{of}\:{h}\:? \\ $$

Commented by mr W last updated on 01/Apr/19

ΔPAB=2×ΔPOA  ΔPOA is minimum if OP=OA  i.e. h=4(√2)

$$\Delta{PAB}=\mathrm{2}×\Delta{POA} \\ $$$$\Delta{POA}\:{is}\:{minimum}\:{if}\:{OP}={OA} \\ $$$${i}.{e}.\:{h}=\mathrm{4}\sqrt{\mathrm{2}} \\ $$

Commented by mr W last updated on 01/Apr/19

Commented by rahul 19 last updated on 02/Apr/19

thank you sir.

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