I know you use the discriminant for this but I am completely lost with the caculation please help.

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# 2002 Winter diet paper 2 Q.10

Started by gary, May 19 2005 02:11 PM

5 replies to this topic

### #1

Posted 19 May 2005 - 02:11 PM

### #2

Posted 19 May 2005 - 02:38 PM

You are given the equation of the circle & the line.

Re-arrange the equation of the line so you have

Substitute this value of y into the equation for the circle.

A line is a tangent to a circle where

5x - (2+4k)x + (k -4) = 0

Now using the discriminant,

That make sense???

Re-arrange the equation of the line so you have

**y= k - 2x**.Substitute this value of y into the equation for the circle.

A line is a tangent to a circle where

**b - 4ac = 0**, so you want to arrange the above equation ang get the following:5x - (2+4k)x + (k -4) = 0

Now using the discriminant,

**b - 4ac = 0**, and factorising you should get that*k = 7*OR*k = -3*and since you are asked to find the value of*k*where**k > 0**you can conclude that the value for k is**k = 7**.That make sense???

### #3

Posted 19 May 2005 - 02:39 PM

I'm stuck on this question to. What is the discriminant?

### #4

Posted 19 May 2005 - 02:46 PM

5x sq - (2+4k)x + (k sq -4) = 0

At this piont, suppose your equation was:

5x sq - (1 + 2k) 2x ....

Wouldn't it make more sense since you've taken out the common factor of 2x, not just x ? Or does the coefficient of x outside the bracket ALWAYS have to be 1?

At this piont, suppose your equation was:

5x sq - (1 + 2k) 2x ....

Wouldn't it make more sense since you've taken out the common factor of 2x, not just x ? Or does the coefficient of x outside the bracket ALWAYS have to be 1?

### #5

Posted 19 May 2005 - 02:51 PM

A quadratic is an expression of the form:

If you try to calculate the discriminant of a quadratic you must have in the above form.

Therefore, your discriminant value would be incorrect as it is the coefficient of the

That make sense??

**ax + bx + c**If you try to calculate the discriminant of a quadratic you must have in the above form.

**a is the coefficient of x****b is the coefficient of x****c is a constant term**Therefore, your discriminant value would be incorrect as it is the coefficient of the

**x term on its own**.That make sense??

### #6

Posted 19 May 2005 - 02:53 PM

Yeah, that makes perfect sense. Thanks!

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