amusgrave3593 amusgrave3593
  • 08-12-2017
  • Mathematics
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Find two values of d such that the line 2x + y = d is tangent to the ellipse 4x2 + y2 = 36. find the points of tangency.

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shinmin
shinmin shinmin
  • 20-12-2017
The solution for this problem would be:
slope must be [ - 2 ]...dy/dx = - 4x / y...= - 2 means y = 2x...thus 4 x² + [ 2x]² = 36 or 
x = ± 3 √2 / 2 and y = ± 3 √2 ---> d = ± 3 √2 ± 3 √2 = ± 6 √2 ...( 3√2 / 2 , 2√3 ) & ( - 3 √2 / 2 , - 3 √2 ) for negative slopes.
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