Question

Find the pole
pole of the line 2x+3y-4=0 with the
respect to the parabola y 2 Use.​

Answer 1

SOLUTION

TO DETERMINE

The pole of the line 2x + 3y - 4 = 0 with the respect to the parabola y² = 4x

EVALUATION

We know that the pole of the line lx + my + n = 0 with the respect to the parabola y² = 4ax is

$\displaystyle \sf{ \bigg( \frac{n}{l} \: \: , \frac{ - 2am}{l} \bigg)}$

Now Comparing the equation 2x + 3y - 4 = 0 with the equation lx + my + n = 0 we get

l = 2 , m = 3 , n = - 4

Again Comparing the equation y² = 4x with the equation y² = 4ax we get a = 1

Hence the required pole

$\displaystyle \sf{ = \bigg( \frac{n}{l} \: \: , \frac{ - 2am}{l} \bigg)}$

$\displaystyle \sf{ = \bigg( \frac{ - 4}{2} \: \: , \frac{ - 2 \times 1 \times 3}{2} \bigg)}$

$\displaystyle \sf{ = ( - 2\: \: , - 3 )}$

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