(^O^|||看到即做)輕鬆StupidMaths=[好趕]

Answers as follows:


1) Let the slope of tangent be "m".

Equation of tangent passing through ( 2 Root ( 10 ), 0 ) is then y = m[ x - 2 Root ( 10 ) ]

Sub y = m[ x - 2 Root ( 10 ) ] into x^2 / 20 + y^2/ 5 = 1

5x^2 + 20m^2 [ x - 2 Root ( 10 ) ]^2 = 100

( 5 + 20m^2 )x^2 - 80m^2 Root ( 10 )x + ( 800m^2 - 100 ) = 0

( 1 + 4m^2 )x^2 - 16m^2 Root ( 10 )x + ( 160m^2 - 20 ) = 0

Solve two "x" in terms of "m", and then find the corresponding "y" using y = m[ x - 2 Root ( 10 ) ].

Use two point-form then to find two equations.


2) Similarly, let the slope of tangent be "m" here.

Equation of tangent passing through ( 0, 1 / Root (2) ) is then y - 1/ Root (2) = m[ x - ( 0 ) ]

m Root (2) x - Root (2) y + 1 = 0

y = [ m Root (2) x + 1 ] / Root (2)

Sub y = [ m Root (2) x + 1 ] / Root (2) into x^2 - 2y^2 = 1

x^2 - [ m Root (2) x + 1 ]^2 = 1

( 1 - 2m )x^2 - 2m Root (2) x - 2 = 0

Solve two "x" in terms of "m", and then find the corresponding "y" using y = [ m Root (2) x + 1 ] / Root (2).

Use two point-form then to find two equations.


P.S.: Since the two given points are both external, hence the questions are more difficult to solve for you need to locate the intersection points between the tangent and the curve first before calculation.


Hope I can help you.




2011-03-06 20:45:22 補充：
Please be reminded that

1/ Root (2) = Root (2) / [ Root (2) ]^2 = Root (2) / 2

Hence, the answer given has no mistake.

For both Q1 and Q2, please show all workings and do until the final answer as u missed out the last part to the final answer.

For Q2, u are wrong, the point that the tangent passes through should be (0,root2/2) instead of (0,root1/2)...Please do again!!!

Re-do please..