The locus of the image of the point `(2,3)` in the line `(x-2y+3)+lambda(2x-3y+4)=0` is`(lambda in R)` (a) `x^2+y^2-3x-4y-4=0` (b) `2x^2+3y^2+2x+4y-7=0` (c) `x^2+y^2-2x-4y+4=0` (d) none of these

Explanation

the given line is `(x-2y+3) + lamda (2x-3y+4)= 0`

as `x-2y=-3`

`2x-3y=-4`

multiplying eqn(2) by 2 and subtracting we get, `y=2`

so, `x=-3+4 = 1`

so point of intersection P is `(1,2)`

`A'` is the reflection of A

as, `AP =BP= A'P`

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