Question

The line 'l_1' passing through the point $(1,1)$ and the 'l_2' passes through the point $(-1,1)$. If the difference of the slope of lines is $2$. Find the locus of the point of intersection of the $l_1$ and $l_2$.

• A. $x^2=y$
• B. $y=2-x^2$
• C. $y^2=x$
• D. $x=2-y^2$

Answer 1

The correct option is A $x^2=y$

REF.Image.

Slope of $L_1=m_1$

slope of $L_2=m_2$

Let P(h,k) $\Rightarrow m_1=\frac{k-1}{h-1}$

$m_2=\frac{k-1}{h+1}$

Given

$m_1-m_2=2$

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

$\Rightarrow (k-1)[\frac{1}{h-1}-\frac{1}{h+1}]=2$

$\Rightarrow (k-1)\left[\frac{2}{h^2-1}\right]=x$

$\Rightarrow h^2-1=k-1\Rightarrow h^2=k$

Locus of P(h,k) is

$x^2=y$