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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
The straight lines
$\dfrac{x}{a} + \dfrac{y}{b} = k$
and
$\dfrac{x}{a} + \dfrac{y}{b} = \dfrac{1}{k}$ (with $k\neq0$)
meet on:
Solution
Intersection point $(x,y)$ satisfies:$\dfrac{x}{a} + \dfrac{y}{b} = k$
$\dfrac{x}{a} + \dfrac{y}{b} = \dfrac{1}{k}$
Subtract → inconsistent unless the meeting point satisfies:
Multiply equations: $\left(\dfrac{x}{a} + \dfrac{y}{b}\right)\left(\dfrac{x}{a} + \dfrac{y}{b}\right) = 1$
Thus locus:
$\left(\dfrac{x}{a} + \dfrac{y}{b}\right)^2 = 1$
This is a pair of parallel lines (degenerate hyperbola) → classified as hyperbola.
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