First slide

Equation of line in Straight lines

Question

$The locus of image of the point (λ^{2}, 2 λ) in the line mirror x - y + 1 = 0 where λ is a parameter is$

Moderate

A

$4 (y + 1) = (x + 1)^{2}$
B

$4 (y - 1) = (x - 1)^{2}$
C

$4 (y + 1) = (x - 1)^{2}$
D

$4 (y - 1) = (x + 1)^{2}$

Solution

$\begin{array}{l} Image of (λ^{2}, 2 λ) in the line mirror x - y + 1 = 0 is \\ \frac{h - λ^{2}}{1} = \frac{k - 2 λ}{- 1} = \frac{- 2 (λ^{2} - 2 λ + 1)}{2} \end{array}$
$\begin{array}{l} \Rightarrow h + 1 = 2 λ \dots \dots \dots \dots \\ And k = λ^{2} + 1 \dots \dots \dots (2) \\ Putting value of λ from (1) into (2), we get \end{array}$
$k - 1 = {(\frac{h + 1}{2})}^{2} l o c u s i s 4 (y - 1) = {(x + 1)}^{2}$

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