The maximum area of the triangle whose sides `a ,b`and `5sintheta),`and `(5sintheta,-5costheta),`where `theta in Rdot`The locus of its orthocentre is`(x+y-1)^2+(x-y-7)^2=100``(x+y-7)^2+(x-y-1)^2=100``(x+y-7)^2+(x+y-1)^2=100``(x+y-7)^2+(x-y+1)^2=100`A. 1B. `1//2`C. 2D. `3//2`

The maximum area of the triangle whose sides `a ,b`and `5sintheta),`an

1.	The maximum area of the triangle whose sides `a ,b`and `5sintheta),`and `(5sintheta,-5costheta),`where `theta in Rdot`The locus of its orthocentre is`(x+y-1)^2+(x-y-7)^2=100``(x+y-7)^2+(x-y-1)^2=100``(x+y-7)^2+(x+y-1)^2=100``(x+y-7)^2+(x-y+1)^2=100`A. 1B. `1//2`C. 2D. `3//2`
Answer» Correct Answer - A Let the vertices be `O(0,0),A(alpha,0)`, and `B(alpha_1,beta_1)`, where `0le alphale1 ` and `1lealpha_(1)^(2)+beta_(1)^(2) le4` So, the area of `DeltaOAB` is maximum where `alpha=1` and `(alpha_1,beta_1)` is (2,0) In this case, `a=1,b=2`, and `c=sqrt5`,which satisfies `2lecle3`. Therefore, the maximum area is 1.

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The maximum area of the triangle whose sides `a ,b`and `5sintheta),`and `(5sintheta,-5costheta),`where `theta in Rdot`The locus of its orthocentre is`(x+y-1)^2+(x-y-7)^2=100``(x+y-7)^2+(x-y-1)^2=100``(x+y-7)^2+(x+y-1)^2=100``(x+y-7)^2+(x-y+1)^2=100`A. 1B. `1//2`C. 2D. `3//2`

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