Consider the ellipse (x^(2))/(16)+(y^(2))/(100)=1 .The tangent to this ellipse at (m, n) has x -intercept A=(a,0) and y- intercept B=(0,b) where a and b are positive. (a) Show that ab=(1600)/(mn) . (b) Use the relationship in part(a) and the fact that (m, n) lies on the ellipse to find the minimum value of ab .

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step-by-step explanation:

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.