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Q.

In the XY – plane, the line $l_{1}$ passes through $(1, 1)$ and line $l_{2}$ passes through $(- 1, 1)$ . If difference of slopes of line is $2,$ the locus of point of intersection of lines $l_{1} & l_{2}$ can be

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a

$y = x^{2}$

b

$y^{2} = x - 2$

c

$y^{2} = x$

d

$y = 2 - x^{2}$

answer is A, B.

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Detailed Solution

Let $P (h, k)$ be the locus

$| m_{1} - m_{2} | = 2 \Rightarrow | \frac{k - 1}{h + 1} - \frac{k - 1}{h - 1} | = 2$

$\Rightarrow k - 1 = \pm (h^{2} - 1)$

Locus is $y = x^{2}, y = 2 - x^{2}$

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In the XY – plane, the line l1 passes through (1,1) and line l2 passes through (−1,1) . If difference of slopes of line is 2, the locus of point of intersection of lines l1&l2 can be