The locus of the point of intersection of the | vedclass

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(C) Given equations are:$bxt - ayt = ab$  --- $(1)$$bx + ay = abt$  --- $(2)$From $(2)$,we have $t = \frac{bx + ay}{ab}$.Substitute $t$ into $(1)$:$bx

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$A$ hyperbola

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(C) Given equations are:$bxt - ayt = ab$  --- $(1)$$bx + ay = abt$  --- $(2)$From $(2)$,we have $t = \frac{bx + ay}{ab}$.Substitute $t$ into $(1)$:$bx(\frac{bx + ay}{ab}) - ay(\frac{bx + ay}{ab}) = ab$Multiply by $ab$:$bx(bx + ay) - ay(bx + ay) = (ab)^2$$(bx - ay)(bx + ay) = (ab)^2$$(bx)^2 - (ay)^2 = (ab)^2$$b^2x^2 - a^2y^2 = a^2b^2$Divide by $a^2b^2$:$\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$This is the standard equation of a hyperbola.

The locus of the point of intersection of the lines $bxt - ayt = ab$ and $bx + ay = abt$ is

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