1 answer

Calculus 1994 AB-3

Question:

1.) Consider the curve defined by x^2+xy+y^2=27
b. Determine whether the lines tangent to the curve at thex-intercepts of the curve are parallel. Show the analysis thatleads to your conclusion. Find the points onthe curve where thelines tangent to the curve are vertical.

Answers

Given equation can be rewritten as the graph of the curve issee that the given equation is an ellipse whose x interceptsare -5.2 and 5.2 at which the tangents drawn are parallel as thederivative of the givenfunction is equal at -5.2 and 5.2so, the slopes of the tangent lines are equal . or thetangents are parallel.further , the y intercepts are -4.7 , 4.7 which whensubstituted in the derivative given the same value.i.e. the slopes of the tangents are equal.∴ the tangents are parallel at the y intercepts..

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