Let the curve C be the mirror image of the parabola y2 = 4x with respect to the line x + y + 4 = 0. If A and B are the points of intersection of C with the line y= – 5, then the distance between A an…

Question

Let the curve C be the mirror image of the parabola y2 = 4x with respect to the line x + y + 4 = 0. If A and B are the points of intersection of C with the line y= – 5, then the distance between A and B is

Accepted Answer

Correct answer: 4. (4) Sol. let P(t2, 2t) be a point on the curve y2 = 4x and Q(h, k) be it’s image in x + y + 4 = 0 h−t^21= k−2 t1=− 2(t^2+2 t+4)2 ⇒ h = –(2t + 4) k = –(t2 + 4) Now k = –5 so t = ±1 hence h = –2, –6 so A, B are (–2, –5) & (–6, –5) Hence AB = 4

$Let the curve C be the mirror image of the parabola y2 = 4x with respect to the line x + y + 4 = 0. If A and B are the points of intersection of C with the line y= - 5, then the distance between A and B is$

Solution

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