the line y=x-c touches the ellipse 9x^2 + 16y^2 = 144. Find the value of c and the coordinate of the point of contact.

a parallelogram is defined by two sets of tangents to the curve x^2 - 4y^2 = 9. The gradients of the tangents are 1 and -1. Find the area of the parallelogram.

1 answer

Please submit one question per post. You have posted two completely different ones here.

Substitute x-c for y in the ellipese equation. Then solve the resulting equation for x, with c as a remining unknown.
Pick the vaue of c that results in one value for x. That will correspond to the tangent-line situation.
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