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in Mathematics by (53.1k points)

The area of the triangle formed by a tangent of slope m to the ellipse x2/a2 + y2/b2 = 1  and the two axes is

(a)  |m|/2 (a2 + b2)

(b)   1/2|m| (a2 + b2)

(c)  |m|/2 (a2m2 + b2)

(d)  1/2|m| (a2m2 + b2)

1 Answer

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by (53.3k points)
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Best answer

Correct option (d)  1/2|m| (a2m2 + b2)

Explanation :

The tangent with slope m is of the form

y = mx + √a2m2 + b2

 Therefore, the intercepts of the tangent on the axes are

-√(a2m2 + b2/m)

and √(a2m2 + b2)

 Hence, the area of the triangle is

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