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Show that the curves y^(2)=4a(x+a) and y...

Show that the curves `y^(2)=4a(x+a) and y^(2)=4b(b-x)(a gt ,b gt 0)` intresect orthogonally.

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Show that the ar5ea enclosed between the parabolas y^(2)=4a(x+a) and y^(2)=4b(b-x) where a gt 0,b gt 0 is (8)/(3)(a+b)sqrt(ab) sq units.

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Knowledge Check

  • Tangent of the angle at which the curve y=a^(x) and y=b^(x) (a ne b gt 0) intersect is give by

    A
    `(log ab)/(1+logab)`
    B
    `(log(a//b))/(1+(loga)(logb))`
    C
    `(logab)/([1+loga]logb)`
    D
    None

  • If a tangent to the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1(a gt b gt 0) having slope 1/3 is a normal to the circle x^(2)+y^(2)+2x+2y+1=0 , then the maximum value of ab is

    A
    `2/3`
    B
    9
    C
    `4/9`
    D
    `1/3`

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