Locus
of the image of the point (2, 3) in the line `(2x-3y""+""4)""+""k""(x-2y""+""3)""=""0,""kepsiR`
, is a :
(1)
straight line parallel to x-axis.
(2) straight line parallel to y-axis
(3)
circle of radius `sqrt(2)`
(4) circle of
radius `sqrt(3)`
Text Solution
AI Generated Solution
To find the locus of the image of the point (2, 3) in the line given by the equation \( (2x - 3y + 4) + k(x - 2y + 3) = 0 \), where \( k \in \mathbb{R} \), we can follow these steps:
### Step 1: Understand the given equation
The equation can be rewritten as:
\[
L = 2x - 3y + 4 + k(x - 2y + 3) = 0
\]
This represents a family of lines parameterized by \( k \).
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