Question

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

• A. an ellipse with equation $\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$
• B. an ellipse with equation $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$
• C. a hyperbola with equation $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$
• D. a hyperbola with equation $\frac{x^2}{b^2}-\frac{y^2}{a^2}=1$

Answer 1

The correct option is C a hyperbola with equation $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

Multiplying both, we get
$(bx{)}^2-(ay{)}^2=(ab{)}^2$

$\Rightarrow \frac{x^2}{a^2}-\frac{y^2}{b^2}=1$,
which is the standard equation of hyperbola