Q)

Asked by araima2001 | 16th Oct, 2016, 09:26: PM

Expert Answer:

Let space space space space straight A left parenthesis straight t subscript 1 right parenthesis identical to left parenthesis at subscript 1 comma space 2 at subscript 1 right parenthesis space comma space space space straight B left parenthesis straight t subscript 2 right parenthesis space identical to left parenthesis at subscript 2 comma space 2 at subscript 2 right parenthesis comma space space straight C left parenthesis straight t subscript 3 right parenthesis identical to left parenthesis at subscript 3 comma space 2 at subscript 3 right parenthesis space space be space the space vertices space of space triangle ABC space inscribed space in space straight y squared equals 4 ax.

area space of space triangle space equals space 1 half open vertical bar straight x subscript 1 open parentheses straight y subscript 2 minus straight y subscript 3 close parentheses plus straight x subscript 2 open parentheses straight y subscript 3 minus straight y subscript 1 close parentheses plus straight x subscript 3 open parentheses straight y subscript 1 minus straight y subscript 2 close parentheses close vertical bar
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 1 half open vertical bar at subscript 1 open parentheses 2 at subscript 2 minus 2 at subscript 3 close parentheses plus straight t subscript 2 open parentheses 2 at subscript 3 minus 2 at subscript 1 close parentheses plus straight t subscript 3 open parentheses 2 at subscript 1 minus 2 at subscript 2 close parentheses close vertical bar
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space fraction numerator 2 straight a squared over denominator 2 end fraction open vertical bar straight t subscript 1 open parentheses straight t subscript 2 minus straight t subscript 3 close parentheses plus straight t subscript 2 open parentheses straight t subscript 3 minus straight t subscript 1 close parentheses plus straight t subscript 3 open parentheses straight t subscript 1 minus straight t subscript 2 close parentheses close vertical bar
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals straight a squared open vertical bar straight t subscript 1 open parentheses straight t subscript 2 minus straight t subscript 3 close parentheses plus straight t subscript 2 open parentheses straight t subscript 3 minus straight t subscript 1 close parentheses plus straight t subscript 3 open parentheses straight t subscript 1 minus straight t subscript 2 close parentheses close vertical bar
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals straight a squared open vertical bar open parentheses straight t subscript 1 minus straight t subscript 2 close parentheses open parentheses straight t subscript 2 minus straight t subscript 3 close parentheses open parentheses straight t subscript 3 minus straight t subscript 1 close parentheses close vertical bar

Answered by Vijaykumar Wani | 17th Oct, 2016, 11:39: AM

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